Question

Prove that the tangent drawn at the ends of any diameter if a circle are parallel

Answer 1

taking  2 tangents
and diameter as transversal
angle A is 90(given)
    and B is 90(given)
they are || because alternative angles on the same side of transversals are supplementary 

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 ⊥ RS and OB ⊥ PQ

∠OAR = 90º

∠OAS = 90º

∠OBP = 90º

∠OBQ = 90º

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