Question

Out of the two concentric circles, the radius of the outer circle is $5cm$ and the chord $AC$ of length $8cm$ is a tangent to the inner circle. Find the radius of the inner circle.

• A. $2cm$
• B. $3cm$
• C. $4cm$
• D. $5cm$

Answer 1

The correct option is B $3cm$

Construction:

Extend OT to P. Then OP becomes the radius of the outer circle $=5$ cm.

By the theorem,

In a circle, if the radius is perpendicular to a chord, then it bisects the chord, we get $AT=TB=4$ cm.

By Pythagoras theorem, in triangle OTB, ${OT}^2+{TB}^2={OB}^2$

$⟹{OT}^2+4^2=5^2⟹{OT}^2=25-16⟹{OT}^2=9⟹OT=3cm$

The radius of the inner circle OT $=3$ cm.