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lOMoARcPSD|35094712 Circles MCQs Mathematics Class10 (University of Kerala) Studocu is not sponsored or endorsed by any college or university Downloaded by Rakesh Kademane1 (rakeshkademane9@gmail.com) lOMoARcPSD|35094712 CIRCLES MULTIPLE-CHOICE QUESTIONS (MCQ) 1. The number of tangent that can be drawn from an external point to a circle is (a) 1 (b) 2 (c) 3 (d) 4 2. In the given figure, RQ is a tangent to the circle with centre O. If SQ = 6 cm and QR = 4 cm, then OR is equal to (a) 30 cm (c) 25 cm 11. In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is O S (b) 3 cm (d) 8 cm (a ) 8 cm T 24 m 3. In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the centre of the circle, then length OP = ? R 7c (a) 2.5 cm (c) 5 cm Q O cm P (b) 28 cm (d) 18 cm 4. Which of the following pairs of lines in a circle cannot be parallel ? (a) two chords (b) a chord and a tangent (c) two tangents (d) two diameters 5. The chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is (a ) 5 2 (b ) 5 2 ( c ) 10 2 6. In the given figure, PT is a tangent to the circle with centre O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is (a) 8 cm (b) 10 cm ( d ) 10 3 T (b) 12 cm A B P (c) 16 cm (d) 136 cm (a ) 9 (c) 353 (b) 15 (d) 25 A O C 13. In the given figure, O is the centre of a circle, AOC is its diameter such that ACB 50 . If AT is the tangent to the circle at the point A then BAT = ? (b) 500 (c) 600 C O 500 B A T (d) 650 6c m (c) 12 cm (d) 16 cm T O (c) 13 cm (d) 15 cm B A Then, BOC is equal to (a) 800 (b) 1000 (c) 1200 O 400 C 14. In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If POQ = 700 , then TPQ is T equal to (a) 350 (c) 550 8. PQ is a tangent to a circle with centre O at the point. If OPQ is an isosceles triangle, then OQP is equal to (a) 300 (b) 450 (c) 600 (d) 900 9. In the given figure, AB and AC are tangents to the circle with centre O suchthat BAC 40 . (b) 14 cm O 12.In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is B (a) 400 O 10 cm P 7. In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent P drawn from P to the circle is 24 cm. Then, the radius of the circle is (a) 10 cm 10. If a chord AB subtends an angle of 600 at the centre of a circle, then the angle between the tangents to the circle drawn from A and B is (a) 300 (b) 600 (c) 900 (d) 1200 ( b) 2 (d) 4 3 16. If PA and PB are two tangents to a circle with centre O such that AOB = 110 0 then APB is equal to (a) 550 (c) 700 O Q (b) 450 (d) 700 15.In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and OTA = 300. Then, AT = ? (a ) 4 ( c) 2 3 P (b) 600 (d) 700 (d) 1400 Downloaded by Rakesh Kademane1 (rakeshkademane9@gmail.com) O A 300 T A O 1100 B P lOMoARcPSD|35094712 24. If PA and PB are two tangents to a circle with centre O such that APB 80 . Then, P m 17. In the given figure, the length of BC is A (a) 7 cm (b) 10 cm 11 cm (c) 14 cm E (d) 15 cm F 3c m 4c AOP ? (a) 400 (c) 600 B C D 18. In the given figure, if AOD = 1350 then BOC is equal to A D A O B (b) 500 (d) 700 25. In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If APQ 58 then the measure of PQB is Q O 1350 B (a) 250 (b) 450 (c) 52.50 O C P A (a) 320 (d) 62.50 19. In the given figure, O is the centre of a circle and PT is the tangent to the circle. If PQ is a chord such that QPT 50 then POQ ? T P (a) 1000 (c) 800 (b) 580 (c) 1220 O 26. In the given figure, O is the centre of the circle. AB is the tangent to the circle at the point P. If PAO 30 then CPB ACP is equal to (a) 60 300 (a) 1500 (b) 300 (c) 600 O (b) 3 3 cm 2 (b) 90 0 (c) 120 the measure of AQB is (d) 900 0 P B (d) 150 0 B B O C 670 21. If two tangents inclined at an angle of 600 are drawn to a circle of radius 3 cm then the length of each tangent is (a )3 cm 0 C 27. In the given figure, PQ is a tangent to a circle with centre O. A is the point of contact. If PAB 67 , A 600 O D Q A P B (d) 1320 500 (b) 900 (d) 750 20. In the given figure, PA and PB are two tangents to the circle with centre O. If APB 60 then OAB is R 580 (c ) 3 3 cm ( d ) 6 cm (a) 73 0 (b) 64 0 P (c) 53 (d) 440 28. In the given figure, two circles touch each other at C and AB is a tangent to both the circles. The measure of ACB is A 22. In the given figure, PQ and PR are tangents to a circle with centre A. If QPA 27 then QAR equals (a) 630 (b) 1170 (c) 1260 (d) 1530 Q A P R 23. In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA PB , then the length of each tanA gent is (a) 3 cm (b) 4 cm C P (c) 5 cm (d) 6 cm B Q A 0 B C (a) 450 (b) 600 (c) 900 (d) 1200 29. O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then, the area of quad. PQOR is O O P (a) 60 cm2 (b) 32.5 cm2 (c) 65 cm2 (d) 30 cm2 Downloaded by Rakesh Kademane1 (rakeshkademane9@gmail.com) R lOMoARcPSD|35094712 P 30. In the given figure, PQR is a tangent to the circle at Q, whose centre is O and AB is a chord parallel to PR such that BQR 70 . Then , AQB ? A B L O (a) 200 (b) 350 0 0 (c) 40 (d) 45 Q R P 31. The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is (a) 8 cm (b) 104 cm (c) 12 cm (d) 125 cm 32. In the given figure, O is the centre of a circle, BOA is its diameter and the tangent at the point P meets BA extended at T. If PBO 30 then PTA ? P (a) 600 (c) 150 (b) 300 (d) 450 B T A O 33. In the given figure, a circle touches the side DF of EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the perimeter of EDF is E D (a) 9 cm (c) 13.5 cm K (b) 12 cm (d) 18 cm H F M 34. To draw a pair of tangents to a circle, which are inclined to each other at an angle of 450 , we have to draw tangents at the end points of those two radii, the angle between which is (a) 1050 (b) 1350 (c) 1400 (d) 1450 35. 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 O Q (a) 17.5 cm (b) 20 cm 38.In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7cm and CS = 3 cm. Then, the length AB = ? S C D (a) 9 cm (b) 10 cm (c) 12 cm (d) 8 cm S O 60 (a) 400 (b) 500 M (c) 600 0 R (d) 700 P 36. In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively.If the area of PQR 189 cm 2 then the length of side PQ is R P A B Q 39.In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 6 cm, BP = 5 cm, CQ = 3 cm and DR = 4 cm then perimeter of quad. ABCD is D 4 cm R C 3 cm (a) 18 cm (b) 27 cm S Q (c) 36 cm (d) 32 cm A 6 cm P 5 cm B 40.In the given figure, O is the cemtre of a circle, AB is a chord and AT is the tangent at A. If AOB 100 then BAT is equal to A (a) 400 (c) 900 Q 500 (d) 25 cm 37.In the given figure, QR is a comQ P R mon tangent to the given circles, touching externally at the point T T. The tangent at T meets QR at P. If PT = 3.8 cm then the length of QR is (a) 1.9 cm (b) 3.8 cm (c) 5.7 cm (d) 7.6 cm SQL 50 and SRM 60 . Then , QSR ? L R T (c) 22.5 cm (b) 500 (d) 1000 O T B 41.In a right triangle ABC, right-angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle is (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm 42.In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10 cm, BC=38 cm, PB = 27 cm and AD CD then the length of CD is Downloaded by Rakesh Kademane1 (rakeshkademane9@gmail.com) lOMoARcPSD|35094712 B P A S 47. In the given figure, three circles with centres A, B, C respectively touch each other externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with centre A is C O Q (a) 11 cm (b) 15 cm (a) 1.5 cm (c) 2.5 cm C R D (c) 20 cm (d) 21 cm 43.In the given figure, ABC is right-angled at B such that BC = 6cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP AB, OQ BC and OR AC . If OP = OQ = A OR = x cm then x = ? 8 cm (b) 2.5 cm (d) 3.5 cm P O X X R X Q 6 cm B C 44.Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm then the length of AD is (a) 3 cm (b) 4 cm (c) 6 cm (d) 7 cm 45.In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and APB 60 . The length of chord AB is A 5 cm (a) 5 2 cm (b) 5 cm P 600 (c) 5 3 cm (d) 7.5 cm R A (b) 10 cm (d) 7.5 cm O B (a ) 5 2 cm (c) 4 10 cm ( b) 3 5 cm (d ) 5 10 cm 46.In the given figure, DE and DF are tangents from an external point D to a circle with centre A. If DE = 5 cm and DE DF then the radius of the circle is (b) 4 cm (d) 6 cm E A B B P C Q 49. In the given figure, O is the centre of two concentric circles of radii 5 cm and 3 cm. From an external point P tangents PA and PB are drawn to these circles. If PA = 12 cm then PB is equal to A B (a) 3 cm (c) 5 cm P 48. In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6cm and BC = 4 cm then the A length of AP is (a) 15 cm (c) 9 cm (a) 2 cm (c) 3 cm Q (b) 2 cm (d) 3 cm D F Downloaded by Rakesh Kademane1 (rakeshkademane9@gmail.com) P
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