Question

Assertion (A): If the PA and PB are tangents drawn to a circle with center O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.
Reason (R): In a cyclic quadrilateral, opposite angles are equal.

• A. Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.
• B. Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain Assertion (A).
• C. Assertion (A) is true but Reason (R) is false.
• D. Assertion (A) is false but Reason (R) is true.

Answer 1

Answer: (C)

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

Answer 2

- The assertion (A) is true: Tangents drawn from an external point to a circle are equal in length, and the angle between the tangent and the radius at the point of contact is $90^\circ$. The quadrilateral formed by the tangents and the radii of the circle from point $P$ is cyclic because the sum of opposite angles equals $180^\circ$, a property of cyclic quadrilaterals.

- The reason (R) is true: In a cyclic quadrilateral, opposite angles are supplementary, meaning the sum of opposite angles is always $180^\circ$.

Since both the assertion and reason are true, and the reason explains the assertion, the correct answer is (a).