MCQOPTIONS
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MCQOPTIONS
This section includes 82 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Two concentric circle have their centres at O. OP = 4 cm and OQ = 5 cm. AB is a chord of the circle and a tangent to the inner circle at P. Find the length of AB. |
| A. | 6 cm |
| B. | 5 cm |
| C. | 8 cm |
| D. | 9 cm |
| Answer» B. 5 cm | |
| 52. |
In the given circle abcd, O is the centre and \[\angle BDC={{42}^{o}}.\]Find the measure of \[\angle ACB.\] |
| A. | \[42{}^\circ \] |
| B. | \[45{}^\circ \] |
| C. | \[48{}^\circ \] |
| D. | \[60{}^\circ \] |
| Answer» D. \[60{}^\circ \] | |
| 53. |
Direction: OA and OB are radii and PA and PB are tangents of the circle, as shown in the given figure. If AP= 15 cm and the radius is 8 cm, find the distance of P from the centre of the circle. |
| A. | 12cm |
| B. | 15cm |
| C. | 17cm |
| D. | 20cm |
| Answer» D. 20cm | |
| 54. |
Fill in the blanks.[a] P chords subtend equal angles at the centre. [b] The arc of a circle subtending a right angle at any point to the circle in the alternating segment is a Q[c] The sum of either pair of the opposite angles of a cyclic quadrilateral is R |
| A. | P Q R Unequal Chord \[{{360}^{o}}\] |
| B. | P Q R Equal Semicircle \[{{180}^{o}}\] |
| C. | P Q R Equal Chord \[{{360}^{o}}\] |
| D. | P Q R Unequal Semicircle \[{{180}^{o}}\] |
| Answer» C. P Q R Equal Chord \[{{360}^{o}}\] | |
| 55. |
In the figure given, \[\overline{DC}\]is produced to E and if \[\overline{AC}\]is the bisector of\[\angle A,\]find the measure of\[\angle BCD.\] |
| A. | \[120{}^\circ \] |
| B. | \[160{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[240{}^\circ \] |
| Answer» D. \[240{}^\circ \] | |
| 56. |
In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are \[AB=6\text{ }cm,\text{ }BC=7\text{ }cm,\]\[CD=4\text{ }cm,\]then AD equals _____. |
| A. | 10 cm |
| B. | 13 cm |
| C. | 11 cm |
| D. | 3 cm |
| Answer» E. | |
| 57. |
O is the centre of the circle having radius 5 cm. AB and AC are two chords such that AB = AC = 6 cm. If OA meets BC at P, then OP = ____. |
| A. | 3.6 cm |
| B. | 1.4 cm |
| C. | 2 cm |
| D. | 3 cm |
| Answer» C. 2 cm | |
| 58. |
In the given figure. ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are drawn. If \[\angle CAD={{40}^{o}}\]and\[\angle BDC={{25}^{o}},\]find \[\angle BCD.\] |
| A. | \[85{}^\circ \] |
| B. | \[120{}^\circ \] |
| C. | \[115{}^\circ \] |
| D. | \[95{}^\circ \] |
| Answer» D. \[95{}^\circ \] | |
| 59. |
In the given figure, OA is a radius and AB is a tangent to the circle. (Note that BC is the shortest distance between B and the circle). lf OA= 12cm and AB = 16 cm, find the distance between B and C. |
| A. | 7cm |
| B. | 6cm |
| C. | 8cm |
| D. | 12cm |
| Answer» D. 12cm | |
| 60. |
Two concentric circles of radii a and b, where \[a>b,\]are given. The length of a chord of the larger circle which touches the other circle is |
| A. | \[\sqrt{{{a}^{2}}-{{b}^{2}}}\] |
| B. | \[2\sqrt{{{a}^{2}}-{{b}^{2}}}\] |
| C. | \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] |
| D. | \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\] |
| Answer» C. \[\sqrt{{{a}^{2}}+{{b}^{2}}}\] | |
| 61. |
In the given figure, \[\angle PQR={{120}^{o}},\]where P, Q and R are points on a circle with centre Then \[\angle OPR\]is ____. |
| A. | \[{{20}^{o}}\] |
| B. | \[{{10}^{o}}\] |
| C. | \[{{30}^{o}}\] |
| D. | \[{{40}^{o}}\] |
| Answer» D. \[{{40}^{o}}\] | |
| 62. |
What is the least number of noncollinear points required to draw a circle passing through them? |
| A. | Two |
| B. | Three |
| C. | Four |
| D. | Nine |
| Answer» C. Four | |
| 63. |
Direction: A \[\Delta \,ABC\] is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure). AB is equal to |
| A. | 13 cm |
| B. | 12 cm |
| C. | 11 cm |
| D. | 14cm |
| Answer» B. 12 cm | |
| 64. |
The parallelogram circumscribing a circle is a |
| A. | Square |
| B. | Rectangle |
| C. | Rhombus |
| D. | Cyclic quadrilateral |
| Answer» D. Cyclic quadrilateral | |
| 65. |
In the figure below, PQ & PR are two tangents to circle. Then. |
| A. | \[\theta =120{}^\circ ,\text{ }\alpha =60{}^\circ \] |
| B. | \[\theta +\alpha =180{}^\circ \] |
| C. | \[\theta =130{}^\circ ,\alpha =50{}^\circ \] |
| D. | \[\theta +\alpha =210{}^\circ \] |
| Answer» C. \[\theta =130{}^\circ ,\alpha =50{}^\circ \] | |
| 66. |
In the figure given above O is the centre of the circle and\[\angle \mathbf{AOD}=\mathbf{10}{{\mathbf{8}}^{{}^\circ }}\], \[\angle \mathbf{BCD}\]is equal to |
| A. | \[{{53}^{{}^\circ }}\] |
| B. | \[{{43}^{{}^\circ }}\] |
| C. | \[{{40}^{{}^\circ }}\] |
| D. | \[{{36}^{{}^\circ }}\] |
| Answer» E. | |
| 67. |
In the given figure above,\[\angle \mathbf{AOB}=\mathbf{4}{{\mathbf{8}}^{{}^\circ }}\], AC and OB Intersect each other at right angles. What is the measure of\[\angle \mathbf{OBC}\] (where, O is the centre of the circle)? |
| A. | \[{{44}^{{}^\circ }}\] |
| B. | \[{{46}^{{}^\circ }}\] |
| C. | \[{{66}^{{}^\circ }}\] |
| D. | \[{{78.5}^{{}^\circ }}\] |
| Answer» D. \[{{78.5}^{{}^\circ }}\] | |
| 68. |
In the given figure above, O is the centre of the circle. The line UTV is a tangent to the circle at T, \[\angle \mathbf{VTR}=\mathbf{5}{{\mathbf{6}}^{{}^\circ }}\]and \[\Delta \mathbf{PTR}\] is an isosceles triangle such that TP = TR. \[\angle \mathbf{x}+\angle \mathbf{y}+\angle \mathbf{z}\]is equal to? |
| A. | \[{{175}^{{}^\circ }}\] |
| B. | \[{{208}^{{}^\circ }}\] |
| C. | \[{{214}^{{}^\circ }}\] |
| D. | \[{{250}^{{}^\circ }}\] |
| Answer» E. | |
| 69. |
In the given figure, AB is a diameter of a circle and CD is perpendicular to AB, if AB=10 cm and \[AE=2\]cm, then what is the length of ED is |
| A. | 5 cm |
| B. | 4cm |
| C. | 10 cm |
| D. | 20 cm |
| Answer» C. 10 cm | |
| 70. |
In the given figure below. O is the centre of the circle. AC and BD intersect at P. If \[\angle \mathbf{AOB}=\mathbf{11}{{\mathbf{0}}^{{}^\circ }}\] and \[\angle \mathbf{DAP}=\mathbf{3}{{\mathbf{0}}^{{}^\circ }}\], then \[\angle \mathbf{APB}\] is equal to |
| A. | \[{{77}^{{}^\circ }}\] |
| B. | \[{{80}^{{}^\circ }}\] |
| C. | \[{{85}^{{}^\circ }}\] |
| D. | \[{{90}^{{}^\circ }}\] |
| Answer» C. \[{{85}^{{}^\circ }}\] | |
| 71. |
Take vertices of a \[\Delta \,ABC\]as centres and draw three circles with centres A, B, C respectively, each touching the other two externally. If the sides of the triangle are AB = a; BC = b, CA = c, find the radii of three circles in terms of a, b, c. |
| A. | \[a+b+c,\frac{a-b-c}{2},\frac{a+b-c}{2}\] |
| B. | \[\frac{a+b}{2},\frac{b+c}{2},\frac{c+a}{2}\] |
| C. | \[\frac{a}{2},\frac{b}{2},\frac{c}{2}\] |
| D. | \[\frac{a-b+c}{2},\frac{a+b-c}{2},\frac{b+c-a}{2}\] |
| Answer» E. | |
| 72. |
If an equilateral triangle ABC is inscribed in a circle and tangents are drawn at their vertices; then what kind of \[\Delta \] is formed by intersection of tangents? |
| A. | An isosceles \[\Delta \] |
| B. | A right angled isosceles \[\Delta \] |
| C. | An acute angled \[\Delta \] |
| D. | An equilateral \[\Delta \] |
| Answer» B. A right angled isosceles \[\Delta \] | |
| 73. |
A tangent PT touches a circle at N. MN is a chord such that \[\angle MNT=63{}^\circ \]. Find \[\angle MON\], where O is the centre of the circle. |
| A. | \[157.5{}^\circ \] |
| B. | \[100{}^\circ \] |
| C. | \[94.5{}^\circ \] |
| D. | \[126{}^\circ \] |
| Answer» E. | |
| 74. |
In the given figure above, O is the centre of the circle, If \[OA=3cm,AC=3cm\] and OX is perpendicular to AC, \[\angle \mathbf{ABC}\] is equal to? |
| A. | \[{{60}^{{}^\circ }}\] |
| B. | \[{{45}^{{}^\circ }}\] |
| C. | \[{{30}^{{}^\circ }}\] |
| D. | None of these |
| Answer» D. None of these | |
| 75. |
Consider the following statements in respect of two chords XY and ZT of a circle intersecting at P. \[\mathbf{PZ}.\mathbf{PY}=\mathbf{PZ}.\mathbf{PT}\] PXZ and PTY are similar triangles. Which of the statements given above is/are correct? |
| A. | Only (i) |
| B. | Only (ii) |
| C. | Both (i) and (ii) |
| D. | None |
| Answer» D. None | |
| 76. |
In the given figure below, AABC is a right angled triangle with AB = 8 cm, BC = 6 cm. O is the in-centre of the triangle. The radius of the in-circle is |
| A. | 3 cm |
| B. | 4 cm |
| C. | 2 cm |
| D. | 5 cm |
| Answer» D. 5 cm | |
| 77. |
From a point P which is at a distance of 15 cm from the centre O of a circle of radius 9 cm, the pair of tangents \[P{{T}_{1}}\] and \[P{{T}_{2}}\] to the circle are drawn. Then, the area of the quadrilateral \[P{{T}_{1}}O{{T}_{2}}\] in \[c{{m}^{2}}\] is |
| A. | 108 |
| B. | 100 |
| C. | 216 |
| D. | 66.5 |
| Answer» D. 66.5 | |
| 78. |
In figure PQ is a chord of the circle and POR is its diameter such that \[\angle PRQ=50{}^\circ \]. If PT is the tangent to the circle at the point P then \[\angle QPT\]is equal to |
| A. | \[45{}^\circ \] |
| B. | \[60{}^\circ \] |
| C. | \[50{}^\circ \] |
| D. | \[55{}^\circ \] |
| Answer» D. \[55{}^\circ \] | |
| 79. |
If radii of two concentric circles are 6 inch and 10 inch, then length of each chord of one circle which is tangent to the other circle is |
| A. | 8 inch |
| B. | 16 inch |
| C. | 20 inch |
| D. | 19 inch |
| Answer» C. 20 inch | |
| 80. |
In the given figure below, ST is a tangent to the circle at F and QR h a diameter of the circle. If\[\angle RPT={{55}^{{}^\circ }}\], then the value of \[\angle SPC\]is |
| A. | \[{{35}^{{}^\circ }}\] |
| B. | \[{{60}^{{}^\circ }}\] |
| C. | \[{{80}^{{}^\circ }}\] |
| D. | \[{{100}^{{}^\circ }}\] |
| Answer» B. \[{{60}^{{}^\circ }}\] | |
| 81. |
In the given figure below. The length of a tangent from an external, point to a circle is \[5\sqrt{3}\] unit. if radius of the circle m 5 units, then the distance of the point from the circle is |
| A. | 5 units |
| B. | 15 units |
| C. | -5 units |
| D. | -15 units |
| Answer» B. 15 units | |
| 82. |
In the given figure below. Two circles intersect at A and B. P is a point on produced RA. PT and PQ are tangents to Itie circles. The relation of PT and PQ is |
| A. | \[PT=2PQ\] |
| B. | \[PT<PQ\] |
| C. | \[PT>PQ\] |
| D. | \[PT=PQ\] |
| Answer» E. | |