Question

In two concentric circles, a chord of length 8 cm of the larger 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=8/2=4cm

In right triangle AOP

$A{O}^2=O{P}^2+P{A}^2$

=> $5^2=O{P}^2+4^2$

=> $O{P}^2=9$

=> OP= 3cm

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