Question

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Answer 1

$PQ$ and $RS$ are tangents

$OA\perp PQ$

and, $OB\perp RS$.

$\angle OAQ=\angle OAP={90}^o$

and, $\angle OBR=\angle OBC={90}^o$

As, $\angle RBO=\angle QAO={90}^o$ [Alternate interior angles]

$\angle PAO=\angle SBO={90}^o$ [Alternate interior angles]

Therefore, $PQ\parallel SR$