Question

Assertion (A)	Reason (R)
If two tangents are drawn to a circle from an external point then they subtend equal angles at the centre.	A parallelogram circumscribing a circle is a rhombus.

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:

Assertion is true. If PA and PB are tangents from external point P touching the circle at A and B, then in ΔOPA and ΔOPB we have OA = OB (radii), PA = PB (tangents from the same external point) and OP common. Hence the triangles are congruent and ∠AOP = ∠BOP, so the two tangents subtend equal angles at the centre.

Reason is also true. If all four sides of a parallelogram touch a circle, tangents from each vertex give equal segment pairs which lead to all sides being equal, so the parallelogram is a rhombus.

The Reason does not explain the Assertion.