Question

Question 4
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Answer 1

Let AB be a diameter of the circle. Two tangents PQ and RS are drawn at points A and B respectively.

Radii of the circle to the tangents will be perpendicular to it.
$\therefore OB\perp RS$ and,
$\therefore OA\perp PQ\angle OBR=\angle OBS=\angle OAP=\angle OAQ={90}^{\circ }$
From the figure,
$\angle OBR=\angle OAQ$ (Alternate interior angles)
$\angle OBS=\angle OAP$ (Alternate interior angles)
Since alternate interior angles are equal, lines PQ and RS will be parallel.
Hence, the tangents drawn at the ends of a diameter of a circle are parallel.