Multiple choice

From an external point $Q$, the length of tangent to a circle is $12$ cm and the distance of $Q$ from the centre of circle is $13$ cm. The radius of circle (in cm) is

  1. $10$
  2. $5$
  3. $12$
  4. $7$
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B Correct answer
Explanation

The radius, tangent, and distance to center form a right triangle where the distance to center is the hypotenuse. r^2 + 12^2 = 13^2. r^2 + 144 = 169. r^2 = 25. r = 5.

AI explanation

The radius, the tangent from the external point, and the line segment joining the point to the center form a right-angled triangle. Using the Pythagorean theorem, the square of the radius equals the square of the distance to the center minus the square of the tangent length. This gives 13 squared minus 12 squared, which is 169 minus 144, equaling 25. The square root of 25 is 5, so the radius of the circle is 5 cm.

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