Question

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

Answer 1

Let $PR$ and $PQ$ be two tangents to the circle with centre $O$ and let $RQ$ be a chord of the circle.

We have to prove that $\angle PQR=\angle PRQ$

Now, $PQ=PR$(Since tangents drawn from an external point to a circle are equal)

In $\Delta PQR$, $\angle PQR=\angle PRQ$

(Since opposite sides are equal, their base angles are also equal)

Hence, proved.