Question

In the adjoining figure, the line MN touches the circle with center A at point M. If AN = 13 and MN = 5, then find the radius of the circle?

Answer 1

In given figure, AM is the radius of the circle.

In ∆AMN, ∠AMN = 90°   ...[Tangent theorem]

∴ AN² = AM² + MN²    ...[Pythagoras theorem]

∴ 13² = AM² + 5²    ...[Given]

∴ 169 = AM² + 25

∴ AM² = 169 – 25

∴ AM² = 144

∴ AM = 12   ...[Taking square root of both sides]

∴ The radius of the circle is 12 units.