Question

Assertion (A): In the given figure, PQ and PR are tangents to a circle centred at О and S is any point on the circle. If ∠QPR = 55° then ∠QSR = 62.5°.

 

Reason (R): If a chord AB subtends an angle of 60° at the centre of a circle then the angle between the tangents at A and B is also 60°.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. The radii to the points of contact are perpendicular to the tangents. Thus, the central angle subtended by QR is 125°, and the angle at the circumference is half of it: ∠QSR = 62.5°.

Step 2 – Reason: R is false. The angle between the tangents is supplementary to the central angle; if the central angle is 60°, the angle between the tangents is 120°, not 60°.