Q. 4 4.3( 319 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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