Question

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

∴ \(AP=PB=\frac{AB}{2}=4cm\)

In right triangle AOP

AO² = OP² + PA²

\(\Rightarrow\) 5² = OP² + 4²

\(\Rightarrow\) OP² = 9

\(\Rightarrow\) OP = 3cm

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