Question

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

Answer 1

Solution to your question

Answer 2

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

Radius drawn to these tangents will be perpendicular to the tangents.

Thus, OA 1 RS and OB 1 PQ

∠OAR = 90°

∠OAS = 90°

∠OBP = 90°

∠OBQ = 90°

It can be observed that

∠OAR = ∠OBQ (Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS will be parallel.