Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

Question

Philoid · Accepted Answer

Consider a circle, In which, PQ is a chord and AP and AQ are two tangents drawn at end points P and Q of the chord.

To Prove: tangent make equal angles with the chord i.e. ∠AQP = ∠APQ

As we know, tangents drawn from an external point are equal

⇒ AP = AQ [Tangents from common external point A]

⇒ ∠AQP = ∠APQ [Angles opposite to equal sides are equal]

Hence, Proved !