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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 done
clear
B)
6 cm done
clear
C)
3 cm done
clear
D)
1 cm done
clear
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question_answer2)
In the given figure, AB is a tangent at P.
Find\[\angle \text{APD}\].
A)
\[\angle \text{PDE}\] done
clear
B)
\[\angle \text{EPB}\] done
clear
C)
\[\angle \text{DPE}\] done
clear
D)
\[\angle \text{PED}\] done
clear
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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 done
clear
B)
5 cm done
clear
C)
8 cm done
clear
D)
9 cm done
clear
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question_answer4)
Find the value of x.
A)
\[\frac{5}{2}\] done
clear
B)
\[\frac{8}{3}\] done
clear
C)
\[\frac{6}{5}\] done
clear
D)
\[\frac{9}{4}\] done
clear
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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 done
clear
B)
4 done
clear
C)
3 done
clear
D)
1 done
clear
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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)
\[\text{AC}+\text{AD}=\text{BD}+\text{CD}\] done
clear
B)
\[\text{AB}+\text{CD}=\text{BC}+\text{AD}\] done
clear
C)
\[\text{AB}+\text{CD}=\text{AC}+\text{BD}\] done
clear
D)
\[~\text{AC}+\text{AD}=\text{BC}+\text{AB}\] done
clear
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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. done
clear
B)
\[\angle \text{PBO}\]and\[\angle \text{APB}\]are complementary angles. done
clear
C)
\[\angle \text{PBO}\]and\[\angle \text{AOB}\] are complementary angles. done
clear
D)
Both [a] and [c] done
clear
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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 done
clear
B)
36 cm done
clear
C)
25 cm done
clear
D)
62 cm done
clear
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question_answer9)
In the figure, find\[\angle \text{ABC}\].
A)
\[\text{6}0{}^\circ \] done
clear
B)
\[\text{12}0{}^\circ \] done
clear
C)
\[\text{18}0{}^\circ \] done
clear
D)
\[\text{9}0{}^\circ \] done
clear
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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 done
clear
B)
Square done
clear
C)
Parallelogram done
clear
D)
Kite done
clear
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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 done
clear
B)
10cm done
clear
C)
12cm done
clear
D)
15cm done
clear
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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. done
clear
B)
PT is the tangent parallel to the chord PQ. done
clear
C)
PT is the tangent parallel to the cord PR. done
clear
D)
S is equidistant from the extremities of the chord. done
clear
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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)
\[\text{3}0{}^\circ \] done
clear
B)
\[\text{45}{}^\circ \] done
clear
C)
\[\text{6}0{}^\circ \] done
clear
D)
\[\text{4}0{}^\circ \] done
clear
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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° done
clear
B)
30° done
clear
C)
60° done
clear
D)
40° done
clear
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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 done
clear
B)
6cm done
clear
C)
8cm done
clear
D)
12cm done
clear
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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. done
clear
B)
Tangent at A is perpendicular to AB. done
clear
C)
Tangent at A is parallel to AC. done
clear
D)
Tangent at A is perpendicular to BC. done
clear
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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)
\[\sqrt{{{d}^{2}}+{{(R-r)}^{2}}}\] done
clear
B)
\[\sqrt{{{d}^{2}}-{{(R+r)}^{2}}}\] done
clear
C)
\[\sqrt{{{(R+r)}^{2}}+{{d}^{2}}}\] done
clear
D)
\[\sqrt{{{d}^{2}}-{{(R-r)}^{2}}}\] done
clear
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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)
\[\text{12}0{}^\circ \] done
clear
B)
\[\text{145}{}^\circ \] done
clear
C)
\[\text{11}0{}^\circ \] done
clear
D)
\[\text{13}0{}^\circ \] done
clear
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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)
\[4\sqrt{6}cm\] done
clear
B)
\[\sqrt{24}\,cm\] done
clear
C)
\[8\sqrt{3}\,cm\] done
clear
D)
\[4\sqrt{3}\,cm\] done
clear
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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 done
clear
B)
12cm done
clear
C)
10cm done
clear
D)
6cm done
clear
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question_answer21)
A If all the sides of a parallelogram touch a circle, what is the parallelogram?
A)
A rectangle done
clear
B)
A rhombus done
clear
C)
A square done
clear
D)
A trapezium done
clear
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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)
\[\text{5}0{}^\circ \] done
clear
B)
\[\text{4}0{}^\circ \] done
clear
C)
\[\text{7}0{}^\circ \] done
clear
D)
\[\text{25}{}^\circ \] done
clear
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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 done
clear
B)
15cm done
clear
C)
17cm done
clear
D)
20cm done
clear
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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 done
clear
B)
15 cm done
clear
C)
30cm done
clear
D)
10cm done
clear
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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)
\[\text{24}{}^\circ \] done
clear
B)
\[\text{144}{}^\circ \] done
clear
C)
\[\text{1}0\text{8}{}^\circ \] done
clear
D)
\[~\text{175}{}^\circ \] done
clear
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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 done
clear
B)
6 cm done
clear
C)
9 cm done
clear
D)
10 cm done
clear
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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 done
clear
B)
10 cm done
clear
C)
21 cm done
clear
D)
200 cm done
clear
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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)
\[\text{68}{}^\circ \] done
clear
B)
\[\text{32}{}^\circ \] done
clear
C)
\[\text{44}{}^\circ \] done
clear
D)
\[\text{96}{}^\circ \] done
clear
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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 done
clear
B)
An equilateral triangle done
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C)
An isosceles triangle done
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D)
A right triangle done
clear
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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 done
clear
B)
15cm done
clear
C)
10cm done
clear
D)
16cm done
clear
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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)
\[\text{3}0{}^\circ \] done
clear
B)
\[\text{4}0{}^\circ \] done
clear
C)
\[~\text{6}0{}^\circ \] done
clear
D)
\[\text{8}0{}^\circ \] done
clear
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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 done
clear
B)
7 cm, 5 cm and 2 cm done
clear
C)
5 cm, 4 cm and 3 cm done
clear
D)
4 cm, 5 cm and 2 cm done
clear
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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)
\[\text{9}0{}^\circ \] done
clear
B)
\[\text{96}{}^\circ \] done
clear
C)
\[\text{1}0\text{8}{}^\circ \] done
clear
D)
\[~\text{12}0{}^\circ \] done
clear
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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)
\[\angle \text{PAQ}=\text{2}\angle \text{OPQ}\] done
clear
B)
\[\angle \text{PAQ}=\angle \text{OPQ}\] done
clear
C)
\[\angle \text{PQA}=\angle \text{QPA}\] done
clear
D)
\[\angle \text{PQA}=\text{2}\angle \text{OPA}\] done
clear
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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 done
clear
B)
10cm done
clear
C)
5cm done
clear
D)
15cm done
clear
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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 done
clear
B)
7cm done
clear
C)
\[8\sqrt{2}\,cm\] done
clear
D)
\[7\sqrt{3}\,cm\] done
clear
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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, \[\text{QR}=(x-2)\text{cm}\], find\[x\]in cm.
A)
6 done
clear
B)
7 done
clear
C)
10 done
clear
D)
14 done
clear
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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 done
clear
B)
4.8 cm done
clear
C)
5.6 cm done
clear
D)
7.4 cm done
clear
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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)
\[15\sqrt{3}\,cm\] done
clear
B)
\[25\sqrt{2}\,cm\] done
clear
C)
\[14\sqrt{2}\,cm\] done
clear
D)
\[30\sqrt{3}\,cm\] done
clear
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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 done
clear
B)
7cm done
clear
C)
4 cm done
clear
D)
2 cm done
clear
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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 done
clear
B)
1 cm, 6 cm, 5 cm done
clear
C)
12 cm, 5 cm, 6 cm done
clear
D)
3cm, 10 cm, 7 cm done
clear
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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 mid-point D and intersects AB at P.
Which of the following is correct?
A)
\[AP=\frac{3}{4}AB\] done
clear
B)
\[AP=\frac{2}{3}AB\] done
clear
C)
\[AP=\frac{4}{5}AB\] done
clear
D)
\[AP=\frac{1}{4}AB\] done
clear
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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)
\[\text{a}{}^\circ +\text{b}{}^\circ =\text{18}0{}^\circ \] done
clear
B)
\[\text{a}{}^\circ +\text{2b}{}^\circ =\text{9}0{}^\circ \] done
clear
C)
\[\text{a}{}^\circ -\text{b}{}^\circ =\text{6}0{}^\circ \] done
clear
D)
\[\text{2a}{}^\circ +\text{b}{}^\circ =\text{1}00{}^\circ \] done
clear
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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)
\[~\text{1}00{}^\circ \] done
clear
B)
\[\text{12}0{}^\circ \] done
clear
C)
\[~\text{9}0{}^\circ \] done
clear
D)
\[~\text{11}0{}^\circ \] done
clear
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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. done
clear
B)
The tangent drawn to the circle at A bisects the side AB. done
clear
C)
The tangent drawn to the circle at B bisects the side AC. done
clear
D)
The tangent drawn to the circle at C bisects the side BC. done
clear
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