Multiple choice

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q, such that OQ = 15 cm. Length of PQ is

  1. 10 √2 cm

  2. 12 cm

  3. 11√9 cm

  4. 13 cm
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A Correct answer
Explanation

Triangle OPQ is a right triangle at P. OQ is the hypotenuse (15), OP is the radius (5). PQ = sqrt(OQ^2 - OP^2) = sqrt(15^2 - 5^2) = sqrt(225 - 25) = sqrt(200) = 10*sqrt(2).

AI explanation

Since the radius is perpendicular to the tangent at the point of contact, triangle OPQ is a right triangle. Applying the Pythagorean theorem gives PQ as the square root of (15^2 - 5^2), which equals the square root of 200. This simplifies to 10 times the square root of 2 cm.

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