Q. 44.4( 410 Votes )

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

Answer :


Let AB is 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 = 90°


OAS = 90°


OBP = 90°


OBQ = 90°


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.


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