Question

The two tangents drawn from an external point to a circle are ______ to the segment joining the centre to the point.

Answer 1

The two tangents drawn from an external point to a circle are equally inclined to the segment joining the centre to the point.

Explanation:

Let O be the centre and P the external point, with tangents PA and PB touching the circle at A and B. Radii OA and OB are perpendicular to the tangents, so triangles OAP and OBP are right triangles with OA = OB and OP common; hence the triangles are congruent and ∠OPA = ∠OPB. Thus the two tangents make equal angles (are equally inclined) with the segment OP.