Question

Length of a tangent segment drawn from a point which is at a distance 15 cm from the centre of a circle is 12 cm, find the diameter of the circle?

Answer 1

Let seg BC be the tangent to the circle with centre A from point C.

∴ AC = 15 cm, BC = 12 cm     ......[Given]

AB is the radius of the circle.

∴ In ∆ABC,

∠ABC = 90°                         ......[Tangent theorem]

∴ AC² = AB² + BC²

∴ (15)² = AB² + (12)²

∴ 225 = AB² + 144

∴ AB² = 225 – 144

∴ AB² = 81

∴ AB = 9                          .....[Taking square root of both sides]

i.e., radius of the circle is 9 cm.

∴ The diameter of the circle is 18 cm.