Q25 of 52 Page 10

Prove that the tangents drawn at the ends of a diameter of a circle are parallel. (CBSE 2012)

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Let Suppose AB is a diameter of the circle with center O,


Now draw two tangents PQ and MN at point A and B respectively.


Radius will be perpendicular to these tangents.


Thus,


OA ⊥ MN and


OB ⊥ PQ


∠OAM = ∠OAN = ∠OBP = ∠OBQ = 90°


Therefore,


∠OAM = ∠OBQ (Alternate interior angles)


∠OAN = ∠OBP (Alternate interior angles)


As alternate interior angles are equal, lines PQ and RS will be parallel to each other.

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