Multiple choice

A line through the circle O of a circle of radius 7 cm cuts the tangent, at a point P on the circles, at Q such that PQ = 24 cm.Find OQ.

  1. 12 cm

  2. 23 cm

  3. 12.5 cm

  4. 25 cm
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D Correct answer
Explanation

The tangent at P is perpendicular to radius OP, so triangle OPQ is right-angled at P. OP = 7 cm (radius), PQ = 24 cm (given). Using Pythagoras theorem: OQ² = OP² + PQ² = 7² + 24² = 49 + 576 = 625. Therefore OQ = sqrt(625) = 25 cm. This is a standard application of tangent-radius property and Pythagoras theorem.

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