Question

In two concentric circles, a chord of length 8 cm of the large circle touches the smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the smaller circle.

Answer 1

We know that the radius and tangent are perpendicular at their point of contact since the perpendicular drawn from the centre bisects the chord.

∴ AP = PB = `(AB)/2` = 4 cm

In the right triangle, AOP

AO² = OP² + PA²

⇒ 5² = OP² + 4²

⇒ OP² = 9

⇒ OP = 3 cm

Hence, the radius of the smaller circle is 3 cm.