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Question:

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

Solution:

PQ and RS are tangents. OA⊥PQ and OB⊥RS. ∠OAQ = ∠OAP = 90° and ∠OBR = ∠OBC = 90°. As ∠RBO = ∠QAO = 90° [Alternate interior angles] ∠PAO = ∠SBO = 90° [Alternate interior angles] Therefore, PQ || SR