Multiple choice

A Point P is 26 cm away from the centre of a circle and the length of the tangent drawn from P to the circle is 24 cm find the radius of the circle.

  1. 11 CM

  2. 10 CM

  3. 16CM

  4. 15 CM
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle formed by the radius, tangent, and distance to center, r^2 + 24^2 = 26^2. r^2 = 676 - 576 = 100, so r = 10.

AI explanation

The radius to the point of tangency is perpendicular to the tangent, forming a right-angled triangle with the radius, the tangent, and the line from the external point to the center. Using the Pythagorean theorem, we square the distance from the center and subtract the square of the tangent length. This gives the radius squared as 26^2 - 24^2 = 676 - 576 = 100, so the radius is 10 cm.

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