{"id":12321,"date":"2024-03-04T10:37:28","date_gmt":"2024-03-04T05:07:28","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=12321"},"modified":"2024-03-05T14:20:07","modified_gmt":"2024-03-05T08:50:07","slug":"ts-10th-class-maths-bits-chapter-9","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-10th-class-maths-bits-chapter-9\/","title":{"rendered":"TS 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle"},"content":{"rendered":"

Solving these\u00a0TS 10th Class Maths Bits with Answers<\/a> Chapter 9 Tangents and Secants to a Circle Bits for 10th Class will help students to build their problem-solving skills.<\/span><\/p>\n

Tangents and Secants to a Circle Bits for 10th Class<\/h2>\n

Question 1.
\nThe angle between the tangent to a circle and the radius drawn through the point of contact is
\nA) 90\u00b0
\nB) 60\u00b0
\nC) 45\u00b0
\nD) 30\u00b0
\nAnswer:
\nA) 90\u00b0<\/p>\n

Question 2.
\nFrom a point P, length of the tangent to a circle is 12 cm and the distance of P from the centre is 13 cm. then the radius of circle is
\nA) 7 cm
\nB) 6 cm
\nC) 5 cm
\nD) 12.5 cm
\nAnswer:
\nC) 5 cm<\/p>\n

Question 3.
\nIf the tangents PA and PB from a point P to a circle with centre ‘O’ are inclined to each other at an angle of 80\u00b0 then \u2220POA = …………..
\nA) 50\u00b0
\nB) 60\u00b0
\nC) 70\u00b0
\nD) 80\u00b0
\nAnswer:
\nA) 50\u00b0<\/p>\n

\"TS<\/p>\n

Question 4.
\nIf TP and TQ are two tangents to a circle with centre ‘O’ so that \u2220POQ = 110\u00b0, then \u2220PTQ =
\nA) 60\u00b0
\nB) 70\u00b0
\nC) 80\u00b0
\nD) 90\u00b0
\nAnswer:
\nB) 70\u00b0<\/p>\n

Question 5.
\nIn the adjacent figure, if quadrilateral PQRS circumscribes a circle then PB + SD = ………………
\n\"TS
\nA) SR
\nB) PR
\nC) QS
\nD) PS
\nAnswer:
\nD) PS<\/p>\n

Question 6.
\nIn the adjacent figure, APB is a tangent to the circle with centre ‘O’ at a point P. If \u2220QPB = 50\u00b0 then the measure of \u2220POQ =
\nA) 25\u00b0
\nB) 75\u00b0
\nC) 100\u00b0
\nD) 120\u00b0
\n\"TS
\nC) 100\u00b0<\/p>\n

Question 7.
\nIn the adjacent figure AB, BC and AC of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 6 cm and AC = 11cm then length of BC =
\nA) 15 cm
\nB) 14 cm
\nC) 7 cm
\nD) 10 cm
\n\"TS
\nAnswer:
\nD) 10 cm<\/p>\n

Question 8.
\nIn the adjacent figure, if BP = 5 cm, QC = 7 cm and AR = 6 cm then AB + BC + AC =
\nA) 18 cm
\nB) 36 cm
\nC) 25 cm
\nD) 30 cm
\n\"TS
\nAnswer:
\nB) 36 cm<\/p>\n

Question 9.
\nThe length of the tangent drawn from a point 17 cm away from the centre of a circle of radius 8 cm is
\nA) 25 cm
\nB) 9 cm
\nC) 15 cm
\nD) 8.5 cm
\nAnswer:
\nC) 15 cm<\/p>\n

\"TS<\/p>\n

Question 10.
\nIn the adjacent figure, the length of the chord AB if PA = 6 cm and \u2220PAB = 60\u00b0 is
\nA) 5 cm
\nB) 6 cm
\nC) 7 cm
\nD) 4 cm
\n\"TS
\nAnswer:
\nB) 6 cm<\/p>\n

Question 11.
\nA line which intersects a circle in two points is called
\nA) a secant
\nB) a tangent
\nC) a chord
\nD) an arc
\nAnswer:
\nA) a secant<\/p>\n

Question 12.
\nThe number of tangents that can be drawn to a circle at any point on it is
\nA) 2
\nB) 1
\nC) 3
\nD) infinetly many
\nAnswer:
\nB) 1<\/p>\n

Question 13.
\nThe number of parallel tangents that can be drawn to a circle can have at the most is
\nA) 1
\nB) 2
\nC) 3
\nD) 4
\nAnswer:
\nB) 2<\/p>\n

\"TS<\/p>\n

Question 14.
\nThe number of tangents that can be drawn to a circle from outside the circles is
\nA) 2
\nB) 1
\nC) infinetly many
\nD) 4
\nAnswer:
\nA) 2<\/p>\n

Question 15.
\nTwo concentric circles of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle
\nA) 10 cm
\nB) 6 cm
\nC) 8 cm
\nD) 2 cm
\nAnswer:
\nC) 8 cm<\/p>\n

Question 16.
\nLength of the arc of a quadrant of a circle of radius ‘r’ is
\nA) \u03c0r
\nB) 3\u03c0r
\nC) \\(\\frac{\\pi \\mathrm{r}}{2}\\) + 2r
\nD) \\(\\frac{\\pi \\mathrm{r}}{2}\\)
\nAnswer:
\nD) \\(\\frac{\\pi \\mathrm{r}}{2}\\)<\/p>\n

Question 17.
\nThe length of the arc A \u00d7 B in the adjacent figure is
\nA) 11 cm
\nB) 22 cm
\nC) 33 cm
\nD) 44 cm
\n\"TS
\nAnswer:
\nB) 22 cm<\/p>\n

\"TS<\/p>\n

Question 18.
\nThe area of a sector of a circle of radius 7 cm and central angle 45\u00b0 is
\nA) 5.5 cm2<\/sup>
\nB) 19.25 cm2<\/sup>
\nC) 154 cm2<\/sup>
\nD) 77 cm2<\/sup>
\nAnswer:
\nB) 19.25 cm2<\/sup><\/p>\n

Question 19.
\nThe measure of central angle of a circle
\nA) 90\u00b0
\nB) 180\u00b0
\nC) 170\u00b0
\nD) 360\u00b0
\nAnswer:
\nD) 360\u00b0<\/p>\n

Question 20.
\nIn the adjacent figure, ‘O’ is the centre of the circle. The area of the sector OAPB is \\(\\frac{5}{18}\\) part of the area of the circle. Then the value
\nA) 30\u00b0
\nB) 60\u00b0
\nC) 45\u00b0
\nD) 100\u00b0
\n\"TS
\nAnswer:
\nD) 100\u00b0<\/p>\n

Question 21.
\nA tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm, then PQ =
\nA) \\(\\sqrt{79}\\)
\nB) \\(\\sqrt{119}\\)
\nC) 119
\nD) 169
\nAnswer:
\nB) \\(\\sqrt{119}\\)<\/p>\n

\"TS<\/p>\n

Question 22.
\nThe number of parallel tangents of a circle with a given tangent is
\nA) 1
\nB) 2
\nC) 3
\nD) 4
\nAnswer:
\nA) 1<\/p>\n

Question 23.
\nThe length of the tangent drawn from an exterior point is 8 cm away from the centre of a circle of radius 6 cm is
\nA) 8 cm
\nB) 10 cm
\nC) 6 cm
\nD) 12 cm
\nAnswer:
\nB) 10 cm<\/p>\n

Question 24.
\nIn the figure x = ………………
\n\"TS
\nA) 60\u00b0
\nB) 100\u00b0
\nC) 110\u00b0
\nD) 120\u00b0
\nAnswer:
\nD) 120\u00b0<\/p>\n

Question 25.
\nThe semi perimeter of \u2206ABC = 28 cm then AF + BD + EC is …………………..
\n\"TS
\nA) 23 cm
\nB) 28 cm
\nC) 56 cm
\nD) 14 cm
\nAnswer:
\nB) 28 cm<\/p>\n

Question 26.
\nThe length of the drawn from a point 8 cm away from the centre of circle with radius 6 cm is
\nA) 2\\(\\sqrt{7}\\) cm
\nB) 3\\(\\sqrt{7}\\) cm
\nC) \\(\\sqrt{7}\\) cm
\nD) 10 cm
\nAnswer:
\nA) 2\\(\\sqrt{7}\\) cm<\/p>\n

\"TS<\/p>\n

Question 27.
\nIn the figure ‘O’ is the centre of the circle and PA, PB are tangents, then their lengths are,
\n\"TS
\nA) 5 cm, 13 cm
\nB) 13 cm, 13 cm
\nC) 13 cm, 12 cm
\nD) 12 cm, 12 cm
\nAnswer:
\nD) 12 cm, 12 cm<\/p>\n

Question 28.
\nAngle in a major segment is
\nA) an obtuse angle
\nB) an acute angle
\nC) right angle
\nD) none
\nAnswer:
\nB) an acute angle<\/p>\n

Question 29.
\nThe length of the tangent drawn to a circle with radius ‘r’ from a point P which is ‘d’ units from the centre is
\nA) \\(\\sqrt{d^2-r^2}\\)
\nB) \\(\\sqrt{r^2+d^2}\\)
\nC) \\(\\sqrt{d r}\\)
\nD) \\(\\sqrt{d + r}\\)
\nAnswer:
\nA) \\(\\sqrt{d^2-r^2}\\)<\/p>\n

Question 30.
\nIf the arc is a minor arc then the segment is a …………………. segment
\nA) Minor
\nB) Major
\nC) Semi-circle
\nD) None
\nAnswer:
\nA) Minor<\/p>\n

\"TS<\/p>\n

Question 31.
\nThe radius of a circle is equal to the sum of the circumferences of two circles of diameters 36 cm and 20 cm is ……………
\nA) 16 cm
\nB) 28 cm
\nC) 42 cm
\nD) 56 cm
\nAnswer:
\nB) 28 cm<\/p>\n

Question 32.
\nIf tangents PA and PB from a point P to a circle with centre ‘O’ are inclined to each other at an angle of 110\u00b0 then \u2220PAO =
\nA) 45\u00b0
\nB) 50\u00b0
\nC) 70\u00b0
\nD) 35\u00b0
\nAnswer:
\nD) 35\u00b0<\/p>\n

Question 33.
\nHow many tangent lines can be drawn to a circle from a point outside the circle ?
\nA) 1
\nB) 4
\nC) 2
\nD) none
\nAnswer:
\nB) 4<\/p>\n

Question 34.
\nIn the given figure \u2220APB = 60\u00b0 and OP = 10 cm. then PA = …………….. cm. (A.P. Mar. ’16, ’15)
\n\"TS
\nA) 5
\nB) 5\\(\\sqrt{2}\\)
\nC) 5\\(\\sqrt{3}\\)
\nD) 20
\nAnswer:
\nC) 5\\(\\sqrt{3}\\)<\/p>\n

\"TS<\/p>\n

Question 35.
\nThe maximum number of possible tangents that can be drawn to a circle is ……………. (A.P. Mar. ’15)
\nA) infinity
\nB) 2
\nC) 4
\nD) 1
\nAnswer:
\nA) infinity<\/p>\n

Question 36.
\nThe angle between the tangent and the radius drawn at the point of contact is ………………. (A.P. June ’15)
\nA) 60\u00b0
\nB) 30\u00b0
\nC) 45\u00b0
\nD) 90\u00b0
\nAnswer:
\nD) 90\u00b0<\/p>\n

Question 37.
\nIf a circle is inscribed in a Quadrilateral then AB + CD = …………….. (A.P. June ’15)
\nA) BC + DA
\nB) AC + BD
\nC) 2AC + 2BD
\nD) 2BC + 2DA
\nAnswer:
\nA) BC + DA<\/p>\n

Question 38.
\nIn the adjoint figure AC = 5, So BC = ………………… cm. (A.P. June ’15)
\n\"TS
\nA) 5 cm
\nB) 7.5 cm
\nC) 2.5 cm
\nD) 10 cm
\nAnswer:
\nC) 2.5 cm<\/p>\n

Question 39.
\nThe angle made at the centre of a circle is ………………. (A.P. Mar. ’16)
\nA) 360\u00b0
\nB) 90\u00b0
\nC) 280\u00b0
\nD) 60\u00b0
\nAnswer:
\nA) 360\u00b0<\/p>\n

\"TS<\/p>\n

Question 40.
\nThe number of secants that can be drawn to a circle is ………………… (T.S. Mar. ’16)
\nA) 2
\nB) 1
\nC) infinity
\nD) 0
\nAnswer:
\nC) infinity<\/p>\n

Question 41.
\nThe diameter of a circle is 10.2 cm then its radius is ……………… cm. (A.P. Mar. ’16)
\nA) 5.1 cm
\nB) 20.4
\nC) 10.5
\nD) 15.3
\nAnswer:
\nA) 5.1 cm<\/p>\n

Question 42.
\nIf \u2018r\u2019 is the radius of a semi-circle then its perimeter is ………………….
\nA) \u03c0r + 2r (or) r[\u03c0 + 2] (or) \\(\\frac{36}{7}\\) r
\nB) \u03c0r + r
\nC) \u03c0r + 3r
\nD) \u03c0r
\nAnswer:
\nA) \u03c0r + 2r (or) r[\u03c0 + 2] (or) \\(\\frac{36}{7}\\) r<\/p>\n

Question 43.
\nWhich of the following is not correct? (A.P. Mar. ’16 )
\ni) Maximum possible tangents that can be drawn to a circle from a point \u2018p\u2019 is 2.
\nii) The number of secants drawn to a circle from a point at exterior is 2.<\/p>\n

A) i only
\nB) ii only
\nC) i and ii
\nD) neither (i) nor (ii)
\nAnswer:
\nA) i only<\/p>\n

\"TS<\/p>\n

Question 44.
\nIn the figure PT is a tangent to the circle with centre O\u2019 then x = ………………….
\n\"TS
\nA) 148\u00b0
\nB) 58\u00b0
\nC) 52\u00b0
\nD) 42\u00b0
\nAnswer:
\nD) 42\u00b0<\/p>\n

Question 45.
\nAngle in a major segment is …………………
\nA) an obtuse angle
\nB) an acute angle
\nC) right angle
\nD) none
\nAnswer:
\nB) an acute angle<\/p>\n

Question 46.
\nIn the figure PT is a tangent drawn from P. If the radius is 7 cm and OP is 25 cm, then the length of the tangent is ………………. cm.
\n\"TS
\nA) 18
\nB) 20
\nC) 24
\nD) 26
\nAnswer:
\nC) 24<\/p>\n

Question 47.
\nPQ is the chord of a circle. The tangent XR drawn at X meets PQ at R when produced. If XR = 12 cm, PQ = x cm, QR = (x – 2) cm. then x = ………………..
\nA) 6 cm
\nB) 7 cm
\nC) 14 cm
\nD) 10 cm
\nAnswer:
\nD) 10 cm<\/p>\n

\"TS<\/p>\n

Question 48.
\nThe angle between the tangent to a circle and the radius drawn through the point of contact is ………………
\nA) 90\u00b0
\nB) 60\u00b0
\nC) 45\u00b0
\nD) 30\u00b0
\nAnswer:
\nA) 90\u00b0<\/p>\n

Question 49.
\nTwo circles intersect at A, B, PS, PT are two tangents drawn from P which lies on AB to the two circles, then ……………..
\n\"TS
\nA) PS = 2PT
\nB) PT = 2PS
\nC) PS = PT
\nD) PS \u2260 PT
\nAnswer:
\nC) PS = PT<\/p>\n

Question 50.
\nIn the figure AB is a diameter and AC is chord of the circle such that \u2220BAC = 30\u00b0. If DC is a tangent, then ABCD is ……………..
\nA) isosceles
\nB) equilateral
\nC) right angled
\nD) acute angled
\nAnswer:
\nA) isosceles<\/p>\n

Question 51.
\nTo draw a pair of tangents to a circle which are inclined to each other at an angle of 60\u00b0 it is required to draw the tangents at the end points of two radii inclined at an angle of ……………….
\nA) 30\u00b0
\nB) 60\u00b0
\nC) 90\u00b0
\nD) 120\u00b0
\nAnswer:
\nD) 120\u00b0<\/p>\n

\"TS<\/p>\n

Question 52.
\nIf the radii of two concentric circles are 5 cm and 13 cm then the length of the chord of one circle which is tangent to the other circle is ……………
\nA) 24 cm
\nB) 18 cm
\nC) 12 cm
\nD) 6 cm
\nAnswer:
\nA) 24 cm<\/p>\n

Question 53.
\nIf tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 110\u00b0 then \u2220PAO = …………….
\nA) 45\u00b0
\nB) 50\u00b0
\nC) 70\u00b0
\nD) 35\u00b0
\nAnswer:
\nD) 35\u00b0<\/p>\n

Question 54.
\nIn a right triangle ABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in the triangle ABC. The radius of the circle is ……………..
\nA) 1cm
\nB) 3 cm
\nC) 5 cm
\nD) 2 cm
\nAnswer:
\nB) 3 cm<\/p>\n

Question 55.
\nThree circles are drawn with the vertices of a triangle as centres such that each circle touches the other two. If the sides of the triangle are 2 cm, 3 cm, 4 cm find the diameter of the smallest circle.
\nA) 4 cm
\nB) 2 cm
\nC) 1 cm
\nD) 5 cm
\nAnswer:
\nC) 1 cm<\/p>\n

\"TS<\/p>\n

Question 56.
\nA circle may have ……………… parallel tangents atmost.
\nA) 10
\nB) 12
\nC) 9
\nD) 2
\nAnswer:
\nD) 2<\/p>\n

Question 57.
\nA tangent to a circle intersects it in ………………. point(s).
\nA) 1
\nB) 2
\nC) 3
\nD) 4
\nAnswer:
\nA) 1<\/p>\n

Question 58.
\nA line segment joining any point on a circle is called its ………………..
\nA) diameter
\nB) tangent
\nC) chord
\nD) none
\nAnswer:
\nC) chord<\/p>\n

Question 59.
\nA line which intersects the given circle at two distinct points is called a ……………….
\nA) tangent
\nB) secant
\nC) circle
\nD) centre
\nAnswer:
\nB) secant<\/p>\n

\"TS<\/p>\n

Question 60.
\nThe common point to a tangent and a circle is called …………………
\nA) point of contact
\nB) circle
\nC) tangent
\nD) none
\nAnswer:
\nA) point of contact<\/p>\n

Question 61.
\nAngle between the tangent and radius drawn through the point of contact is ……………..
\nA) 100\u00b0
\nB) 70\u00b0
\nC) 80\u00b0
\nD) 90\u00b0
\nAnswer:
\nD) 90\u00b0<\/p>\n

Question 62.
\nThe circumference of a circle is 100 cm. The side of a square inscribed in the circle is ……………… cm.
\nA) \\(\\frac{1}{\\pi}\\)
\nB) \\(\\frac{5 \\sqrt{2}}{\\pi}\\)
\nC) \\(\\frac{50 \\sqrt{2}}{\\pi}\\)
\nD) 50\\(\\sqrt{2}\\)
\nAnswer:
\nC) \\(\\frac{50 \\sqrt{2}}{\\pi}\\)<\/p>\n

Question 63.
\nThe area of a square inscribed in a circle of radius 8 cm is …………………… cm2<\/sup>.
\nA) 118
\nB) 129
\nC) 160
\nD) 128
\nAnswer:
\nD) 128<\/p>\n

\"TS<\/p>\n

Question 64.
\nThe area of a circle that can be inscribed in a square of side 6 cm is …………………… cm2<\/sup>.
\nA) 9\u03c0
\nB) 12\u03c0
\nC) 120\u03c0
\nD) none
\nAnswer:
\nA) 9\u03c0<\/p>\n

Question 65.
\nThe perimeter of a quadrant of a circle of radius \\(\\frac{7}{2}\\) cm is …………………. cm.
\nA) 9.5
\nB) 12.5
\nC) 10.5
\nD) 2
\nAnswer:
\nB) 12.5<\/p>\n

Question 66.
\nThe number of tangents at one point of a circle is ………………..
\nA) 1
\nB) 2
\nC) 3
\nD) 10
\nAnswer:
\nA) 1<\/p>\n

Question 67.
\nNumber of tangents to a circle which are parallel to a secant are …………………
\nA) 1
\nB) 10
\nC) 9
\nD) 2
\nAnswer:
\nD) 2<\/p>\n

\"TS<\/p>\n

Question 68.
\n………………. tangent can be drawn from a point inside a circle.
\nA) No
\nB) 1
\nC) 4
\nD) None
\nAnswer:
\nA) No<\/p>\n

Question 69.
\nA line which is perpendicular to the radius of the circle through the point of contact is called a …………………..
\nA) secant
\nB) tangent
\nC) chord
\nD) none
\nAnswer:
\nB) tangent<\/p>\n

Question 70.
\nThe tangents drawn at the ends of a diameter are ………………
\nA) parallel
\nB) 0
\nC) perpendicular
\nD) none
\nAnswer:
\nB) 0<\/p>\n

Question 71.
\nThe tangent drawn at the end point of radius is ………………….
\nA) 0
\nB) parallel
\nC) perpendicular
\nD) none
\nAnswer:
\nC) perpendicular<\/p>\n

\"TS<\/p>\n

Question 72.
\nTangents drawn from an exterior point are ……………..
\nA) not equal
\nB) parallel
\nC) equal
\nD) none
\nAnswer:
\nC) equal<\/p>\n

Question 73.
\nA secant meets a circle in ……………… points.
\nA) 2
\nB) 4
\nC) 3
\nD) 1
\nAnswer:
\nA) 2<\/p>\n

Question 74.
\nA tangent meets a circle in ……………… points.
\nA) 10
\nB) 9
\nC) 7
\nD) 1
\nAnswer:
\nD) 1<\/p>\n

Question 75.
\nSum of the central angles in a circle is ………………..
\nA) 360\u00b0
\nB) 300\u00b0
\nC) 180\u00b0
\nD) 110\u00b0
\nAnswer:
\nA) 360\u00b0<\/p>\n

\"TS<\/p>\n

Question 76.
\nAngle is a semi-circle at the centre is …………………….
\nA) 100\u00b0
\nB) 180\u00b0
\nC) 200\u00b0
\nD) 80\u00b0
\nAnswer:
\nB) 180\u00b0<\/p>\n

Question 77.
\nFrom the figure, x = ……………… cm.
\n\"TS
\nA) 8.4
\nB) 8.8
\nC) 4.8
\nD) 4
\nAnswer:
\nC) 4.8<\/p>\n

Question 78.
\nAngle in a semi-circle is ……………..
\nA) 80\u00b0
\nB) 90\u00b0
\nC) 100\u00b0
\nD) 110\u00b0
\nAnswer:
\nB) 90\u00b0<\/p>\n

Question 79.
\nNumber of tangents drawn to a circle is ……………….
\nA) 1
\nB) 4
\nC) 3
\nD) infinite
\nAnswer:
\nD) infinite<\/p>\n

\"TS<\/p>\n

Question 80.
\nIn the figure, x = ……………….. cm.
\n\"TS
\nA) 5
\nB) 6
\nC) 8.2
\nD) 10
\nAnswer:
\nA) 5<\/p>\n

Question 81.
\nAngle in a minor segment is ………………
\nA) acute
\nB) 60\u00b0
\nC) obtuse
\nD) none
\nAnswer:
\nC) obtuse<\/p>\n

Question 82.
\nIn a circle d = 10.2 cm then r = …………… cm.
\nA) 4.1
\nB) 5.1
\nC) 4.6
\nD) 5.6
\nAnswer:
\nB) 5.1<\/p>\n

Question 83.
\nThe longest chord in a circle is ……………..
\nA) diameter
\nB) radius
\nC) chords
\nD) none
\nAnswer:
\nA) diameter<\/p>\n

\"TS<\/p>\n

Question 84.
\nCircles having same centre are called ……………. circles.
\nA) triangle
\nB) concentric
\nC) trapezium
\nD) none
\nAnswer:
\nB) concentric<\/p>\n

Question 85.
\nCircles having same radii are ………………
\nA) congruent
\nB) not congruent
\nC) only similar
\nD) none
\nAnswer:
\nA) congruent<\/p>\n

Question 86.
\nArea of circle is ………….. sq. units.
\nA) \\(\\frac{\\pi}{\\mathrm{r}^2}\\)
\nB) \u03c0r3<\/sup>
\nC) \u03c0r2<\/sup>
\nD) \u03c02<\/sup>r2<\/sup>
\nAnswer:
\nC) \u03c0r2<\/sup><\/p>\n

Question 87.
\nThe shaded portion represents ……………….
\n\"TS
\nA) minor segment
\nB) major segment
\nC) chord
\nD) none
\nAnswer:
\nA) minor segment<\/p>\n

\"TS<\/p>\n

Question 88.
\nArea of semi-circle is ……………….
\nA) \u03c0r2<\/sup>
\nB) \u03c02<\/sup> r
\nC) \\(\\frac{\\pi \\mathrm{r}^2}{2}\\)
\nD) \u03c0r
\nAnswer:
\nC) \\(\\frac{\\pi \\mathrm{r}^2}{2}\\)<\/p>\n

Question 89.
\nNumber of circle passing through 3 collinear points in a plane is ……………….
\nA) 1
\nB) 0
\nC) 9
\nD) 12
\nAnswer:
\nB) 0<\/p>\n

Question 90.
\nSum of opposite angles in a cyclic quadrilateral is …………….
\nA) 100\u00b0
\nB) 180\u00b0
\nC) 190\u00b0
\nD) 200\u00b0
\nAnswer:
\nB) 180\u00b0<\/p>\n

Question 91.
\nCyclic rhombus is a ………………
\nA) rhombus
\nB) parallelogram
\nC) triangle
\nD) none
\nAnswer:
\nA) rhombus<\/p>\n

\"TS<\/p>\n

Question 92.
\nIn the figure, \u2220BAC = ………………
\n\"TS
\nA) 90\u00b0
\nB) 70\u00b0
\nC) 30\u00b0
\nD) none
\nAnswer:
\nC) 30\u00b0<\/p>\n

Question 93.
\nArea of sector = ……………….
\nA) \\(\\frac{x^{\\circ}}{360}\\) \u00d7 \u03c0r2<\/sup>
\nB) \\(\\frac{x^{\\circ}}{360}\\) \u00d7 2\u03c0r
\nC) lb
\nD) none
\nAnswer:
\nA) \\(\\frac{x^{\\circ}}{360}\\) \u00d7 \u03c0r2<\/sup><\/p>\n

Question 94.
\nArea of ring = ……………….
\nA) \u03c0(R2<\/sup> – r2<\/sup>)
\nB) \u03c0(R – r)
\nC) R2<\/sup> – r2<\/sup>
\nD) \u03c0(R2<\/sup> – r2<\/sup> + 2r)
\nAnswer:
\nA) \u03c0(R2<\/sup> – r2<\/sup>)<\/p>\n

\"TS<\/p>\n

Question 95.
\nSide of a square is 4 cm then A = ……………….. cm2<\/sup>.
\nA) 64
\nB) 12
\nC) 16
\nD) 20
\nAnswer:
\nC) 16<\/p>\n

Question 96.
\nDiameter of a circle passes through ……………
\nA) equal
\nB) point
\nC) centre
\nD) none
\nAnswer:
\nC) centre<\/p>\n

Question 97.
\nThe shaded portion represents …………… segment.
\n\"TS
\nA) major
\nB) minor
\nC) acute
\nD) none
\nAnswer:
\nA) major<\/p>\n

Question 98.
\nWhich of the following is a semicircle ?
\n\"TS
\nAnswer:
\n(A)<\/p>\n

Question 99.
\nAngles in the same segment of the circle ………………
\nA) 30\u00b0
\nB) equal
\nC) not equal
\nD) none
\nAnswer:
\nB) equal<\/p>\n

\"TS<\/p>\n

Question 100.
\nIn the figure, x\u00b0 = …………
\n\"TS
\nA) 30\u00b0
\nB) 110\u00b0
\nC) 60\u00b0
\nD) none
\nAnswer:
\nD) none<\/p>\n

Question 101.
\nIn the figure, x = …………………
\n\"TS
\nA) 20\u00b0
\nB) 90\u00b0
\nC) 60\u00b0
\nD) 80\u00b0
\nAnswer:
\nC) 60\u00b0<\/p>\n

Question 102.
\nArea of triangle = ………………. sq.units.
\nA) bh
\nB) \\(\\frac{1}{2}\\)bh
\nC) \\(\\frac{\\mathrm{b}+\\mathrm{h}}{2}\\)
\nD) none
\nAnswer:
\nB) \\(\\frac{1}{2}\\)bh<\/p>\n

\"TS<\/p>\n

Question 103.
\nArea of square whose is 3 cm in …………………… cm2<\/sup>.
\nA) 6
\nB) 12
\nC) 10
\nD) 9
\nAnswer:
\nD) 9<\/p>\n

Question 104.
\nArea of circle with radius r = …………………
\nA) \u03c0r4<\/sup>
\nB) \u03c0r
\nC) \u03c0r2<\/sup>
\nD) \\(\\frac{\\pi}{2}\\)
\nAnswer:
\nC) \u03c0r2<\/sup><\/p>\n

Question 105.
\nThe area of square is 49 cm2<\/sup> then side is …………….. cm.
\nA) 12
\nB) 6
\nC) 8
\nD) 7
\nAnswer:
\nD) 7<\/p>\n

Question 106.
\nIn the above problem perimeter = ……………. cm.
\nA) 19
\nB) 16
\nC) 28
\nD) none
\nAnswer:
\nC) 28<\/p>\n

\"TS<\/p>\n

Question 107.
\nAngle made by minute hand in 1 m = ………………..
\nA) 6\u00b0
\nB) 12\u00b0
\nC) 10\u00b0
\nD) none
\nAnswer:
\nA) 6\u00b0<\/p>\n

Question 108.
\nx\u00b0 = 60\u00b0, r = 14 cm then area of sector = ………………. cm2<\/sup>.
\nA) 100.6
\nB) 102.66
\nC) 811.6
\nD) none
\nAnswer:
\nB) 102.66<\/p>\n

Question 109.
\nArea of regular hexagon of side ‘a’ units is ……………… sq. units.
\nA) \\(\\frac{6 \\sqrt{3}}{4}\\)a2<\/sup>
\nB) \\(\\frac{6 \\sqrt{3}}{7}\\)a2<\/sup>
\nC) \\(\\frac{6}{7} \\sqrt{3}\\)a2<\/sup>
\nD) none
\nAnswer:
\nA) \\(\\frac{6 \\sqrt{3}}{4}\\)a2<\/sup><\/p>\n

Question 110.
\nParallelogram circumscribing a circle is a ……………
\nA) parallelogram
\nB) rhombus
\nC) circle
\nD) none
\nAnswer:
\nB) rhombus<\/p>\n

\"TS<\/p>\n

Question 111.
\nIn the figure, XY and X1<\/sup>Y1<\/sup> are two parallel tangents to a circle with centre ‘O’ and another tangent AB with point of contact C intersecting XY at A and X1<\/sup>Y1<\/sup> at B then \u2220AOB = ………………..
\n\"TS
\nA) 75\u00b0
\nB) 95\u00b0
\nC) 70\u00b0
\nD) 90\u00b0
\nAnswer:
\nD) 90\u00b0<\/p>\n

Question 112.
\nThe angle between a tangent to a circle and the radius drawn at the point of contact is ……………….
\nA) 60\u00b0
\nB) 70\u00b0
\nC) 90\u00b0
\nD) 20\u00b0
\nAnswer:
\nC) 90\u00b0<\/p>\n

Question 113.
\nIf AP and AQ are the two tangents to a circle with centre ‘O’. So that POQ = 110\u00b0 then \u2220PAQ = ……………..
\n\"TS
\nA) 70\u00b0
\nB) 60\u00b0
\nC) 65\u00b0
\nD) 75\u00b0
\nAnswer:
\nA) 70\u00b0<\/p>\n

Question 114.
\nArea of circle interms of diameter is ……………..
\nA) \\(\\frac{\\pi \\mathrm{d}^2}{4}\\)
\nB) \u03c0r2<\/sup>
\nC) \\(\\frac{\\pi \\mathrm{d}^2}{14}\\)
\nD) all
\nAnswer:
\nA) \\(\\frac{\\pi \\mathrm{d}^2}{4}\\)<\/p>\n

\"TS<\/p>\n

Question 115.
\nIn the figure, AP = 12 cm, PB = 16 cm and \u03c0 = 3.14 then perimeter of shaded region is …………………… cm.
\n\"TS
\nA) 51
\nB) 70
\nC) 58
\nD) 68
\nAnswer:
\nC) 58<\/p>\n

Question 116.
\nA bicycle wheel makes 75 revolutions per minute to maintain a speed of 8.91 km per hour then diameter of the wheel is ………………. m.
\nA) 6.3
\nB) 0.63
\nC) 8.1
\nD) none
\nAnswer:
\nB) 0.63<\/p>\n

Question 117.
\nAngle described by hour hand in 12 hours is ………………….
\nA) 90\u00b0
\nB) 200\u00b0
\nC) 360\u00b0
\nD) 180\u00b0
\nAnswer:
\nC) 360\u00b0<\/p>\n

Question 118.
\nEach angle in a square is …………….
\nA) 85\u00b0
\nB) right angle
\nC) 60\u00b0
\nD) 70\u00b0
\nAnswer:
\nB) right angle<\/p>\n

\"TS<\/p>\n

Question 119.
\nIn the figure, the area of shaded region is ……………… cm2<\/sup>.
\n\"TS
\nA) 74
\nB) 60
\nC) 82
\nD) 42
\nAnswer:
\nD) 42<\/p>\n

Question 120.
\nPerimeter of semicircle is ………… units.
\nA) \\(\\frac{36 \\mathrm{r}}{7}\\)
\nB) \\(\\frac{18}{7}\\)r
\nC) \\(\\frac{9}{17}\\)r
\nD) none
\nAnswer:
\nA) \\(\\frac{36 \\mathrm{r}}{7}\\)<\/p>\n

Question 121.
\nIn the figure the relation among a, b and c is ………………
\n\"TS
\nA) c2<\/sup> = a2<\/sup> + b2<\/sup>
\nB) c2<\/sup> – a2<\/sup> = 2b2<\/sup>
\nC) c2<\/sup> + b2<\/sup> = a2<\/sup>
\nD) all
\nAnswer:
\nA) c2<\/sup> = a2<\/sup> + b2<\/sup><\/p>\n

Question 122.
\nIn the figure, a = ……………….
\n\"TS
\nA) 100\u00b0
\nB) 170\u00b0
\nC) 80\u00b0
\nD) 90\u00b0
\nAnswer:
\nC) 80\u00b0<\/p>\n

Question 123.
\nPerimeter of sectors = …………….
\nA) l + 2r
\nB) l – r
\nC) l – 2r
\nD) none
\nAnswer:
\nA) l + 2r<\/p>\n

Question 124.
\nWhat do you observe from the below
\n\"TS
\nA) PA < PB B) PA > PB
\nC) PA = PB
\nD) none
\nAnswer:
\nC) PA = PB<\/p>\n

\"TS<\/p>\n

Question 125.
\nThe radius of a circle is doubled then its area becomes ……………… times.
\nA) 5
\nB) 4
\nC) 9
\nD) none
\nAnswer:
\nB) 4<\/p>\n","protected":false},"excerpt":{"rendered":"

Solving these\u00a0TS 10th Class Maths Bits with Answers Chapter 9 Tangents and Secants to a Circle Bits for 10th Class will help students to build their problem-solving skills. Tangents and Secants to a Circle Bits for 10th Class Question 1. The angle between the tangent to a circle and the radius drawn through the point … Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/12321"}],"collection":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/comments?post=12321"}],"version-history":[{"count":1,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/12321\/revisions"}],"predecessor-version":[{"id":12420,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/12321\/revisions\/12420"}],"wp:attachment":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/media?parent=12321"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/categories?post=12321"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/tags?post=12321"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}