Mock Test – Circles

1. Two parallel lines touch the circle at points A and B respectively. If area of the circle is 25 π cm², then AB is equal to

2. In figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is

3. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): If the length of a tangent from an external point to a circle is 10 cm, then the length of the other tangent from the same point is 10 cm.
Reason (R): Tangent drawn from a external point to a circle an equal in lengths.

4. 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

5. In the given figure, TP and TQ are two tangents to a circle with centre O, such that POQ = 110°. Then PTQ is equal to

6. In the given figure, AB and AC are tangents to the circle with centre O such that BAC = 40°, then BOC is equal to

7. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): If the angle between two tangents drawn from an external point P to a circle of radius 5 cm and centre O is 90°, then length of each tangent is 10 cm.
Reason (R): Opposite angles of a cyclic quadrilateral an supplementary.

8. In the figure PA and PB are tangents to the circle with centre O. If APB = 60°, then OAB is

9. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): If the radius of a circle is 5 cm and distance of a point outside the circle from its centre is 13 cm, then the length of the tangent drawn from
that external point to the circle is 12 cm.
Reason (R): In a circle, tangent is always perpendicular to its radius at the point of contact.

10. In figure if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and BQR = 70°, then AQB is equal to

11. In figure if O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then POQ is equal to

12. A line through point of contact and passing through centre of circle is known as

13. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): If two tangent are drawn from an external point P to a circle at points A and B, then ΔPA B is an equilateral Δ, when ∠APB = 60°.
Reason (R): The measure of each angle of an equilateral triangle is 60°.

14. In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is

15. In figure AT is a tangent to the circle with centre O such that OT = 4 cm and OTA = 30°. Then AT is equal to

16. In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre.
Reason (R): In a triangle, angles opposite to equal sides are unequal.

17. A circle touches x-axis at A and y-axis at B. If O is origin and OA = 5 units, then diameter of the circle is

18. In figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If AOB = 100°, then BAT is equal to

19. In figure, PQ and PR are tangents to a circle with centre A. If QPA = 27°, then QAR equals to

20. C (O, r₁) and C(O, r₂) are two concentric circles with r₁ > r₂. AB is a chord of C(O, r₁) touching C(O, r₂) at C then