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.