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Question

Prove that, tangents drawn to the end points of diameter of the circle are parallel to each other.

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Solution

Given: AB is the diameter of the circle with center O.

Two tangents PQ and RS are drawn at points B and A respectively.

Proof:

The radius is perpendicular to these tangents.

That is, OA RS and OB PQ

OAR=OAS=OBP=OBQ=90o

OAR=OBQ (Alternate interior angles)

OAS=OBP (Alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS are parallel.

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