Question

prove that tagents drawn at the ends of diameter of circle are parllel

Answer 1

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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.

See the diagram in the picture

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