Multiple choice

A tangent PQ at a point P of a circle of radius 7 cm meets a line through centre O at a point Q so that OQ = 25 cm length PQ is

  1. 20 cm

  2. 14 cm

  3. 24 cm

  4. 26 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A tangent is perpendicular to the radius at the point of contact. This forms a right triangle OPQ with hypotenuse OQ = 25 and leg OP = 7. PQ^2 = OQ^2 - OP^2 = 25^2 - 7^2 = 625 - 49 = 576. PQ = 24.

AI explanation

Because the radius is perpendicular to the tangent at point P, triangle OPQ is a right triangle. Using the Pythagorean theorem, PQ equals the square root of (25^2 - 7^2), which simplifies to 24 cm.

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