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question_answer1)
In the given figure, PT touches the circle at R whose centre is O. Diameter SQ when produced meets PT at P. Given \[\angle SPR={{x}^{o}}\]and \[\angle QRP={{y}^{o}}\]. Then,
A)
\[{{x}^{o}}+2{{y}^{o}}={{90}^{o}}\] done
clear
B)
\[2{{x}^{o}}+{{y}^{o}}={{90}^{o}}\] done
clear
C)
\[{{x}^{o}}+{{y}^{o}}={{120}^{o}}\] done
clear
D)
\[3{{x}^{o}}+2{{y}^{o}}={{120}^{o}}\] done
clear
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question_answer2)
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 done
clear
B)
13 cm done
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C)
11 cm done
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D)
3 cm done
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question_answer3)
In the given figure, a circle touches the side SC of \[\Delta ABC\]at P and touches AB and /AC produced at Q and R respectively. If \[AQ=5\,cm,\] find the perimeter of \[\Delta ABC\].
A)
11 cm done
clear
B)
10 cm done
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C)
6 cm done
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D)
7 cm done
clear
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question_answer4)
In the given figure, AB and PQ intersect at M. If A and B are centres of circles then ____.
A)
\[PM=MQ\] done
clear
B)
\[PQ\bot AB\] done
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C)
Both (A) and (B) done
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D)
\[PQ=AB\] done
clear
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question_answer5)
BC is the diameter of a semicircle. The sides AB and AC of a triangle ABC meet the semicircle at P and Q respectively. PQ subtends \[{{140}^{o}}\]at the centre of the semicircle. Then \[\angle A\] is _____.
A)
\[{{10}^{o}}\] done
clear
B)
\[{{20}^{\text{o}}}\] done
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C)
\[{{30}^{o}}\] done
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D)
\[{{40}^{o}}\] done
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question_answer6)
Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is _____.
A)
\[\sqrt{7}\,cm\] done
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B)
\[3\sqrt{7}\,cm\] done
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C)
\[4\sqrt{7}\,cm\] done
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D)
\[(8+2\sqrt{7})\,cm\] done
clear
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question_answer7)
In the given figure, ABCD is a cyclic quadrilateral and PQ is tangent to the circle with centre '0'. BD is diameter. \[\angle DCO={{40}^{o}},\] \[\angle ABD={{60}^{o}}\]. Then \[\angle BCP=\] _____.
A)
\[{{50}^{o}}\] done
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B)
\[{{100}^{o}}\] done
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C)
\[{{60}^{o}}\] done
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D)
\[{{20}^{o}}\] done
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question_answer8)
In the following figure, PT is of length 8 cm. OP is 10 cm. Then the radius of the circle is _____.
A)
2 cm done
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B)
18 cm done
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C)
(5/4) cm done
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D)
6 cm done
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question_answer9)
A circle inscribed in \[\Delta \,ABC\] having \[AB=10\text{ }cm,\]\[BC=12\text{ }cm,\text{ }CA=28\text{ }cm\]touching sides at D, E, F (respectively). Then \[AD+BE+CF\]is _____.
A)
25 cm done
clear
B)
20 cm done
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C)
22 cm done
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D)
18 cm done
clear
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question_answer10)
In the given figure, O is the centre of the circle, then \[\angle XOZ\] is _____.
A)
\[2\angle XZY\] done
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B)
\[2\angle Y\] done
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C)
\[2\angle Z\] done
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D)
\[2(\angle XZY+\angle YXZ)\] done
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question_answer11)
In the given figure, O is the centre and SAT is a tangent to the circle at A. If\[\angle BAT=30{}^\circ ,\] find \[\angle AOB\] and \[\angle AQB\].
A)
\[{{60}^{o}},{{150}^{o}}\] done
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B)
\[{{30}^{o}},{{150}^{o}}\] done
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C)
\[{{60}^{o}},{{60}^{o}}\] done
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D)
None of these done
clear
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question_answer12)
In the given figure, O is the centre of the circle. Determine \[\angle ABC\] and Reflex\[\angle AOC\]
A)
\[{{68}^{o}}.\text{ }{{136}^{o}}\] done
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B)
\[{{68}^{o}}.\text{ }{{68}^{o}}\] done
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C)
\[{{68}^{o}}.\text{ 22}{{\text{4}}^{o}}\] done
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D)
\[{{34}^{o}}.\text{ 13}{{\text{6}}^{o}}\] done
clear
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question_answer13)
In the given figure, O is the centre of the circle. If PA and PB are tangents, then the value of \[\angle AQB\] is
A)
\[{{100}^{o}}\] done
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B)
\[{{80}^{o}}\] done
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C)
\[{{60}^{o}}\] done
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D)
\[{{50}^{o}}\] done
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question_answer14)
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)
\[\sqrt{{{a}^{2}}-{{b}^{2}}}\] done
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B)
\[2\sqrt{{{a}^{2}}-{{b}^{2}}}\] done
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C)
\[\sqrt{{{a}^{2}}+{{b}^{2}}}\] done
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D)
\[2\sqrt{{{a}^{2}}+{{b}^{2}}}\] done
clear
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question_answer15)
In figure, there are two concentric circles, with centre O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP == 12 cm, find the length of BP.
A)
12 cm done
clear
B)
\[12.65\text{ }cm\] done
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C)
\[12.36\,cm\] done
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D)
\[12.56\,cm\] done
clear
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question_answer16)
Let s denote the semi perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, find BD.
A)
\[s-b\] done
clear
B)
\[2s+h\] done
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C)
\[b+s\] done
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D)
\[3b-s\] done
clear
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question_answer17)
In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. lf \[\angle PBT={{30}^{o}},\] then \[BA:AT\]is
A)
\[3:1\] done
clear
B)
\[4:1\] done
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C)
\[2:1\] done
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D)
\[3:2\] done
clear
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question_answer18)
A circle with centre O touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Find\[\angle AOD+\angle BOC.\].
A)
\[{{90}^{o}}\] done
clear
B)
\[{{180}^{o}}\] done
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C)
\[{{160}^{o}}\] done
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D)
\[{{100}^{o}}\] done
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question_answer19)
How many tangents can a circle have?
A)
1 done
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B)
2 done
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C)
4 done
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D)
Infinite done
clear
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question_answer20)
If O is the centre of a circle, AOC is its diameter and B is a point an the circle such that\[\angle ACB={{50}^{o}}\]. If AT is the tangent to the circle at the point A, then \[\angle BAT=\]
A)
\[{{40}^{o}}\] done
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B)
\[{{50}^{o}}\] done
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C)
\[{{60}^{o}}\] done
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D)
\[{{65}^{o}}\] done
clear
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question_answer21)
In the given figure, A and B are the centres of two circles that intersect at X and V. PXQ is a straight line. If reflex angle \[QBY={{210}^{o}},\]find obtuse angle PAY.
A)
\[{{210}^{o}}\] done
clear
B)
\[{{150}^{o}}\] done
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C)
\[{{160}^{o}}\] done
clear
D)
\[{{120}^{o}}\] done
clear
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question_answer22)
AB is a chord of length 24 cm of a circle of radius 13 cm. The tangents at A and B intersect at a point C. Find the length AC.
A)
\[31.2\,cm\] done
clear
B)
\[12\,cm\] done
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C)
\[28.8\text{ }cm\] done
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D)
\[25\text{ }cm\] done
clear
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question_answer23)
A)
(a) \[\to \] (p), (b) \[\to \] (r), (c) \[\to \] (q) done
clear
B)
(a) \[\to \] (r), (b) \[\to \] (q), (c) \[\to \] (p) done
clear
C)
(a) \[\to \] (q), (b) \[\to \] (r), (c) \[\to \] (p) done
clear
D)
(a) \[\to \] (r), (b) \[\to \] (p), (c) \[\to \] (q) done
clear
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question_answer24)
The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length AD.
A)
19 cm done
clear
B)
20 cm done
clear
C)
16 cm done
clear
D)
\[\sqrt{150}\,cm\] done
clear
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question_answer25)
In the given figure, O is the centre of a circle; PQL and PRM are the tangents at the points Q and R respectively and S is a point on the circle such that \[\angle SQL={{50}^{o}}\]and \[\angle SRM={{60}^{o}}\]. Then, find \[\angle QSR\] and \[\angle RPQ\].
A)
\[{{40}^{o}},{{140}^{o}}\] done
clear
B)
\[{{50}^{o}},{{140}^{o}}\] done
clear
C)
\[{{60}^{o}},{{120}^{o}}\] done
clear
D)
\[{{70}^{o}},\text{ }{{40}^{o}}\] done
clear
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