Prove that the range ts drawn at the ends of a diameter of a circle ar

1.	Prove that the range ts drawn at the ends of a diameter of a circle are parallel
Answer» Let\xa0AB 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 = 90ºIt can be observed that∠OAR = ∠OBQ\xa0(Alternate interior angles)∠OAS = ∠OBP\xa0(Alternate interior angles)Since\xa0alternate interior angles are equal, lines PQ and RS will be parallel.

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