Question

The lengths of two tangents drawn from an external point to a circle are ______.

Answer 1

The lengths of two tangents drawn from an external point to a circle are equal.

Explanation:

Let P be the external point and PA, PB the tangents touching the circle at A and B. Radii OA and OB are each perpendicular to the tangents, so ∠OAP and ∠OBP are right angles. In right triangles OAP and OBP, the hypotenuse OP is common and OA = OB (radii). By RHS congruence the triangles are congruent, so PA = PB.