
question_answer1) PT is a tangent and PAB is a secant of the circle meeting the circle at A and B. If PA = 4 cm and AB = 5 cm. What is the length of PT?
A) 8 cm
B) 6 cm
C) 3 cm
D) 1 cm
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question_answer2) In the given figure, AB is a tangent at P. Find\[\angle \text{APD}\].
A) \[\angle \text{PDE}\]
B) \[\angle \text{EPB}\]
C) \[\angle \text{DPE}\]
D) \[\angle \text{PED}\]
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question_answer3) 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
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question_answer4) Find the value of x.
A) \[\frac{5}{2}\]
B) \[\frac{8}{3}\]
C) \[\frac{6}{5}\]
D) \[\frac{9}{4}\]
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question_answer5) What is the number of common tangents that can be drawn to two intersecting circles touching at two points?
A) 2
B) 4
C) 3
D) 1
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question_answer6) If the four sides of a quadrilateral ABCD are tangential to a circle, which of the following is true?
A) \[\text{AC}+\text{AD}=\text{BD}+\text{CD}\]
B) \[\text{AB}+\text{CD}=\text{BC}+\text{AD}\]
C) \[\text{AB}+\text{CD}=\text{AC}+\text{BD}\]
D) \[~\text{AC}+\text{AD}=\text{BC}+\text{AB}\]
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question_answer7) In the given figure, OA and OB are two radii of the circle. If PA and PB are tangents to the circle at A and B respectively which is the correct statement?
A) \[\angle \text{AOB}\]and\[\angle \text{APB}\] are the supplementary angles.
B) \[\angle \text{PBO}\]and\[\angle \text{APB}\]are complementary angles.
C) \[\angle \text{PBO}\]and\[\angle \text{AOB}\] are complementary angles.
D) Both [a] and [c]
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question_answer8) AP is a secant and PT is a tangent to a circle. Lf PT=15cm and AB = 8BP, find AP.
A) 45 cm
B) 36 cm
C) 25 cm
D) 62 cm
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question_answer9) In the figure, find\[\angle \text{ABC}\].
A) \[\text{6}0{}^\circ \]
B) \[\text{12}0{}^\circ \]
C) \[\text{18}0{}^\circ \]
D) \[\text{9}0{}^\circ \]
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question_answer10) If OA and OB are radii and PA and PB are tangents to the circle, which of the following is quadrilateral OAPB?
A) Rectangle
B) Square
C) Parallelogram
D) Kite
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question_answer11) In the given figure, a circle touches the side BC of\[\Delta \text{ABC}\]at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of\[\Delta \text{ABC}\].
A) 6cm
B) 10cm
C) 12cm
D) 15cm
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question_answer12) A tangent ST at P to a circle at P is parallel to a chord QR of the circle. Which of the following is correct statement?
A) P is equidistant from the extremities of the chord.
B) PT is the tangent parallel to the chord PQ.
C) PT is the tangent parallel to the cord PR.
D) S is equidistant from the extremities of the chord.
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question_answer13) In the given figure.TP and TQ are tangents to the circle. If\[\angle \text{PAQ}=\text{7}0{}^\circ \], what is\[\angle \text{PTQ}\]?
A) \[\text{3}0{}^\circ \]
B) \[\text{45}{}^\circ \]
C) \[\text{6}0{}^\circ \]
D) \[\text{4}0{}^\circ \]
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question_answer14) AB is a diameter of a circle with centre O. Tangent ST touches the circle at C. If \[\angle ~\text{BAC}=\text{4}0{}^\circ \], find\[\angle \text{ACT}\].
A) 50?
B) 30?
C) 60?
D) 40?
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question_answer15) 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
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question_answer16) An isosceles triangle in which AB = AC is inscribed in a circle. Which of the following is true?
A) Tangent at A is parallel to BC.
B) Tangent at A is perpendicular to AB.
C) Tangent at A is parallel to AC.
D) Tangent at A is perpendicular to BC.
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question_answer17) If the distance between two circles of radii R and r is d, find the length of the direct common tangent.
A) \[\sqrt{{{d}^{2}}+{{(Rr)}^{2}}}\]
B) \[\sqrt{{{d}^{2}}{{(R+r)}^{2}}}\]
C) \[\sqrt{{{(R+r)}^{2}}+{{d}^{2}}}\]
D) \[\sqrt{{{d}^{2}}{{(Rr)}^{2}}}\]
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question_answer18) A tangent ST, touches a circle at B.AB is a chord such that \[\angle \text{ABT}=\text{65}{}^\circ \] Find\[\angle \text{AOB}\], where O is the centre of the circle.
A) \[\text{12}0{}^\circ \]
B) \[\text{145}{}^\circ \]
C) \[\text{11}0{}^\circ \]
D) \[\text{13}0{}^\circ \]
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question_answer19) In the given figure, two circles with centres A and B of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of segment AB meets the bigger circle in P and Q, find the length of PQ.
A) \[4\sqrt{6}cm\]
B) \[\sqrt{24}\,cm\]
C) \[8\sqrt{3}\,cm\]
D) \[4\sqrt{3}\,cm\]
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question_answer20) In the given figure, 0 is the centre of the circle. PQ is the tangent to the circle and secant PAB passes through the centre O. If PQ =5 cm and PA = 1 cm, find the radius of the circle.
A) 8cm
B) 12cm
C) 10cm
D) 6cm
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question_answer21) A If all the sides of a parallelogram touch a circle, what is the parallelogram?
A) A rectangle
B) A rhombus
C) A square
D) A trapezium
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question_answer22) Direction: OA and OB are radii and PA and PB are tangents of the circle, as shown in the given figure. Find \[\angle \text{APB}\]if\[\angle \text{OPB}=\text{25}{}^\circ \].
A) \[\text{5}0{}^\circ \]
B) \[\text{4}0{}^\circ \]
C) \[\text{7}0{}^\circ \]
D) \[\text{25}{}^\circ \]
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question_answer23) 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
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question_answer24) Direction: OA and OB are radii and PA and PB are tangents of the circle, as shown in the given figure. If PB = 20 cm and OA = 15 cm, find the shortest distance between the circle and P.
A) 25 cm
B) 15 cm
C) 30cm
D) 10cm
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question_answer25) Direction: OA and OB are radii and PA and PB are tangents of the circle, as shown in the given figure. If\[\angle \text{APO}=\text{18}{}^\circ \], find \[\angle \text{AOB}\].
A) \[\text{24}{}^\circ \]
B) \[\text{144}{}^\circ \]
C) \[\text{1}0\text{8}{}^\circ \]
D) \[~\text{175}{}^\circ \]
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question_answer26) PQ is a chord of a circle, which on producing, meets the tangent TR at R. If PQ = 5 cm and QR = 4 cm, find TR.
A) 3 cm
B) 6 cm
C) 9 cm
D) 10 cm
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question_answer27) Two circles of radii 8 cm and 2 cm have direct common tangent of length 10 cm, find the distance between their centres.
A) 8 cm
B) 10 cm
C) 21 cm
D) 200 cm
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question_answer28) BD and CD are two tangents drawn to a circle with centre O. If\[\angle \text{BDC}=\text{44}{}^\circ \],find\[\angle \text{BAC}\].
A) \[\text{68}{}^\circ \]
B) \[\text{32}{}^\circ \]
C) \[\text{44}{}^\circ \]
D) \[\text{96}{}^\circ \]
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question_answer29) If an equilateral triangle ABC is inscribed in a circle, which of the following is formed by the tangents at their vertices?
A) A scalene triangle
B) An equilateral triangle
C) An isosceles triangle
D) A right triangle
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question_answer30) In the given figure, ABCD is a quadrilateral in which\[\angle \text{Q }=\text{ 9}0{}^\circ \]. A circle C (O, r) touches the sides AB, BC, CD and DA at P, Q, R, S respectively. If BC = 38 cm, CD = 25 cm, and BP = 27 cm, find the value of r.
A) 14cm
B) 15cm
C) 10cm
D) 16cm
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question_answer31) In the given circle, O is the centre, QP is a diameter and PT is a tangent. If \[\angle \text{QOS}=\text{12}0{}^\circ \], find \[\angle \text{PTS}\].
A) \[\text{3}0{}^\circ \]
B) \[\text{4}0{}^\circ \]
C) \[~\text{6}0{}^\circ \]
D) \[\text{8}0{}^\circ \]
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question_answer32) With the vertices of a \[\Delta \text{ABC}\] as centres, three circles are described, each touching the other two externally. If the sides of the triangle are 9 cm, 7 cm and 6 cm, find the radii of the circles.
A) 4 cm, 7 cm and 3 cm
B) 7 cm, 5 cm and 2 cm
C) 5 cm, 4 cm and 3 cm
D) 4 cm, 5 cm and 2 cm
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question_answer33) A, B and C are three points on a circle. The tangent at C meets BA produced at T. Given that \[\angle \text{ATC}=\text{36}{}^\circ \]and \[\angle \text{ACT}=\text{48}{}^\circ \], find the angle subtended by AB at the centre of the circle.
A) \[\text{9}0{}^\circ \]
B) \[\text{96}{}^\circ \]
C) \[\text{1}0\text{8}{}^\circ \]
D) \[~\text{12}0{}^\circ \]
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question_answer34) Tangents AP and AQ are drawn to a circle with centre 0 from an external point A. Identify the correct statement.
A) \[\angle \text{PAQ}=\text{2}\angle \text{OPQ}\]
B) \[\angle \text{PAQ}=\angle \text{OPQ}\]
C) \[\angle \text{PQA}=\angle \text{QPA}\]
D) \[\angle \text{PQA}=\text{2}\angle \text{OPA}\]
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question_answer35) PT and QT are tangents drawn to the circle with centre O. If OT= 25 cm and OP = 15cm, find QT.
A) 20cm
B) 10cm
C) 5cm
D) 15cm
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question_answer36) Two circles with centres 0 and P, and radii 8 cm and 4 cm touch each other externally. Find the length of their common tangent QR.
A) 8cm
B) 7cm
C) \[8\sqrt{2}\,cm\]
D) \[7\sqrt{3}\,cm\]
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question_answer37) PQ is a chord of a circle .the tangent XR at X on the circle cuts PQ produced at R. If\[\text{XR}=\text{12 cm}\],\[\text{PQ }=x\] cm, \[\text{QR}=(x2)\text{cm}\], find\[x\]in cm.
A) 6
B) 7
C) 10
D) 14
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question_answer38) A circle with centre 0 is inscribed in an isosceles triangle PQR in which PQ = PR= 17 cm and QR = 16 cm. Find the radius of the circle.
A) 6.2 cm
B) 4.8 cm
C) 5.6 cm
D) 7.4 cm
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question_answer39) A circle with centre 0 and radius 5 cm is inscribed in an equilateral triangle ABC. Find the perimeter of\[\Delta \text{ABC}\].
A) \[15\sqrt{3}\,cm\]
B) \[25\sqrt{2}\,cm\]
C) \[14\sqrt{2}\,cm\]
D) \[30\sqrt{3}\,cm\]
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question_answer40) ABC is a right  angled triangle with\[\angle \text{B}=\text{9}0{}^\circ \], AB=12cm and AC=13cm.A circle with centre 0 is inscribed inside the triangle. Find the radius of the circle.
A) 8cm
B) 7cm
C) 4 cm
D) 2 cm
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question_answer41) Three circles with centres A,B and C touch one another externally. The three centres are joined to one another to form a triangle. If AB = 7 cm, BC = 11 cm and AC = 6 cm, find the radii of the three circles.
A) 2 cm, 7 cm, 9 cm
B) 1 cm, 6 cm, 5 cm
C) 12 cm, 5 cm, 6 cm
D) 3cm, 10 cm, 7 cm
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question_answer42) In the given figure, ABC is an isosceles triangle in which AB = AC.A circle through B touches AC at its midpoint D and intersects AB at P. Which of the following is correct?
A) \[AP=\frac{3}{4}AB\]
B) \[AP=\frac{2}{3}AB\]
C) \[AP=\frac{4}{5}AB\]
D) \[AP=\frac{1}{4}AB\]
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question_answer43) A tangent CQ touches a circle with centre O at P. Diameter AB is produced to meet the tangent at C. If \[\angle \text{ACP}=\text{a}{}^\circ \]and\[\angle \text{BPC}=\text{b}{}^\circ \], find the relation connecting a and b.
A) \[\text{a}{}^\circ +\text{b}{}^\circ =\text{18}0{}^\circ \]
B) \[\text{a}{}^\circ +\text{2b}{}^\circ =\text{9}0{}^\circ \]
C) \[\text{a}{}^\circ \text{b}{}^\circ =\text{6}0{}^\circ \]
D) \[\text{2a}{}^\circ +\text{b}{}^\circ =\text{1}00{}^\circ \]
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question_answer44) In the given figure, 0 is the centre of in circle inscribed in\[\Delta \text{ABC}\]. Find \[\angle \text{BOC}\]if\[\angle \text{BAC}=\text{4}0{}^\circ \].
A) \[~\text{1}00{}^\circ \]
B) \[\text{12}0{}^\circ \]
C) \[~\text{9}0{}^\circ \]
D) \[~\text{11}0{}^\circ \]
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question_answer45) In \[\Delta \text{ABC},\text{ }\angle \text{B}=90{}^\circ \].If a circle drawn with AB as diameter intersects the hypotenuse AC at P, which of the following is true?
A) The tangent drawn to the circle at P bisects the side BC.
B) The tangent drawn to the circle at A bisects the side AB.
C) The tangent drawn to the circle at B bisects the side AC.
D) The tangent drawn to the circle at C bisects the side BC.
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