Question

Assertion (A): In the given figure, the quadrilateral PQRS circumscribes a circle. Then, PA + CS = PS.

Reason (R): The tangents drawn at the end points of a diameter of a circle are parallel to each other.

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 but Reason (R) is not a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. Tangents drawn to a circle from the same external point are equal. Thus, the tangent segments from the relevant vertices give $$PA = PD$$ and $$CS = DS$$. Since $$PS = PD + DS$$, it follows that $$PS = PA + CS$$.

Step 2 – Reason: R is true. The tangents at the endpoints of a diameter are each perpendicular to the diameter, so they are parallel.

Step 3 – Link: R is a true fact about tangents, but it does not explain the equality in A. Assertion (A) follows from the equality of tangents drawn from the same external point.