Question

Prove that in any circle, the tangents at two points make equal angles with the chord joining the points of contact.

Answer 1

Given: A circle with centre O

PA and PB are tangents to the circle through a point P and AB is the chord.

We know that lengths of tangents drawn from a point outside the circle are equal.

∴ PA = PB

In ΔPAB, PA = PB

We know that angles opposite to equal sides are equal in measure.

∴ ∠PBA = ∠PAB

Thus, in a circle, the tangents at two points make equal angles with the chord joining the points of contact.