Below you will find MCQ Questions of Chapter 10 Circles Class 10 Maths that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 10 MCQ Questions with answers will widen your skills and understand concepts in a better manner.
MCQ Questions for Class 10 Maths Chapter 10 Circles with answers
1. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
(a) 60 cm^{2}
(b) 65 cm^{2}
(c) 30 cm^{2}
(d) 32.5 cm^{2}
► (a) 60 cm^{2}
2. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such ∠POR = 120°, then ∠OPQ is
(a) 45°
(b) 30°
(c) 60°
(d) 35°
► (b) 30°
3. A line that intersects a circle in exactly one point is called a
(a) Diameter
(b) Tangent
(c) Radius
(d) Chord
► (b) Tangent
4. In fig, O is the centre of the circle, CA is tangent at A and CB is tangent at B drawn to the circle. If ∠ACB = 75°, then ∠AOB =
(a) 75°
(b) 85°
(c) 95°
(d) 105º
► (d) 105º
5. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80∘, then find ∠POA.
(a) 60°
(b) 100°
(c) 40°
(d) 50°
► (d) 50°
6. A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is x cm. The value of x =
(a) 20 cm
(b) 24 cm
(c) 18 cm
(d) 12 cm
► (b) 24 cm
7. A tangent PQ at a point P o a circle of radius 5 cm meets a line through the centre O at point Q, so that OQ = 12 cm. find the length PQ.
(a) √113 cm
(b) 13 cm
(c) √119 cm
(d) 26 cm
► (c) √119 cm
8. From a point X, the length of the tangent to a circle is 20 cm and the distance of X from the centre is 25 cm. The radius of the circle is
(a) 10 cm
(b) 5√41 cm
(c) 15 cm
(d) 20 cm
► (c) 15 cm
9. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°, then ∠OPQ is
(a) 60°
(b) 45°
(c) 30°
(d) 90°
► (c) 30°
10. In the given figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°, then ∠BOC is equal to
(a) 40°
(b) 50°
(c) 140°
(d) 150°
► (c) 140°
11. In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle. Find TQ : TR
(a) 8 : 7
(b) 7 : 8
(c) 5 : 4
(d) 1 : 1
► (d) 1 : 1
12. A tangent PA is drawn from an external point P to a circle of radius 3√2 cm such that the distance of the point P from O is 6 cm as shown figure. The value of ∠APO is
(a) 30°
(b) 60°
(c) 45°
(d) 75°
► (c) 45°
13. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ = 12 cm. Length PQ is
(a) 12 cm
(b) 13 cm
(c) 8.5 cm
(d) √119 cm
► (d) √119 cm
14. Two circle touch each other externally at C and AB is a common tangent to the circles. Then, ∠ACB =
(a) 60°
(b) 45°
(c) 30°
(d) 90°
► (d) 90°
15. Number of tangents, that can be drawn to a circle, parallel to a given chord is
(a) 3
(b) Zero
(c) Infinite
(d) 2
► (d) 2
16. The distance between two parallel tangents to a circle of radius 5 cm is
(a) 5cm
(b) 8cm
(c) 10cm
(d) 9cm
► (c) 10cm
17. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
(a) 7 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm.
► (a) 7 cm
18. A tangent to a circle is a line that intersects the circle in
(a) Exactly one point
(b) 2 points
(c) 3 points
(d) 4 points
► (a) Exactly one point
Hope the given MCQ Questions will help you in cracking exams with good marks. These Circles MCQ Questions will help you in practising more and more questions in less time.