Multiple choice

choose the correct option and give justification. from a point $Q$, the length of the tangent to a circle is 24 cm and the distance of $Q$ from the centre is $25\ cm$. The radius of the circle is

  1. $7\ cm$
  2. $12\ cm$
  3. $15\ cm$
  4. $24.5\ cm$
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A Correct answer
Explanation

The tangent to a circle is perpendicular to the radius at the point of contact. This forms a right-angled triangle with the radius, tangent, and distance from the center as the hypotenuse. Using Pythagoras theorem, r^2 + 24^2 = 25^2, so r^2 = 625 - 576 = 49, meaning r = 7 cm.

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