Question

Assertion (A): If PA and PB are tangents drawn from an external point P to а circle with centre O then the quadrilateral AOBP is cyclic.

Reason (R): The angle between two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

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

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

Explanation:

Step 1 – Assertion: A is true. The angle between the tangents and the central angle subtended by the points of contact are supplementary. Hence, the opposite angles of quadrilateral AOBP are supplementary, so it is cyclic.

Step 2 – Reason: R is true. It states that the angle between two tangents is supplementary to the central angle subtended by the segment joining their points of contact.

Step 3 – Link: R directly gives the supplementary opposite angles needed to show that AOBP is cyclic, so it correctly explains A.