Question

prove that tangents drawn at the ends of a diameter of a circle are parallel to each other.

Answer 1

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The answer to your question is there in the link below..

https://www.youtube.com/watch?v=KOXQZFAaGj8

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Answer 2

Here AB is a diameter of the circle with centre O, two tangents PQ and RS drawn at points A and B respectively.
Radius will be perpendicular to these tangents.

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = ∠OAS = ∠OBP = ∠OBQ = 90º

Therefore,

∠OAR = ∠OBQ (Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

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