Question

Tangents drawn from an external point to a circle subtend ______ angles to the centre.

Answer 1

Tangents drawn from an external point to a circle subtend equal angles to the centre.

Explanation:

Let tangents AP and AQ from external point A touch the circle at P and Q and let O be the centre. OP and OQ are radii and are perpendicular to AP and AQ, so ∠OPA = ∠OQA = 90°. In right triangles OPA and OQA, OP = OQ (radii) and OA = OA (common), so the triangles are congruent (RHS). Hence ∠POA = ∠QOA — the tangents subtend equal angles at the centre.