Area between circles

Denote the centre of both the circles as $O$ . Join $PO$ and let it intersect the smaller circle at $C$ and $D$ where $C$ is closer to $A$ than to $B$ .

Let the radius of the larger circle be $R$ and the smaller circle be $r$ .

By power of a point , $PC \cdot PD = (PO-CO) \cdot (PO+OD) = (R-r)(R+r) = R^2-r^2 = PA \cdot PB = 18$ .

Area of the region between the two concentric circles is $\pi(R^2-r^2) = 18 \pi \approx \boxed{56.55}$ .

We know that PA.PB =PT^2. On carefully observing we find that PT^2 is nothing but R^2-r^2=18 So area between circles =22/7 ×18=56.57 { area between circles =pi(R^2-r^2}

Cheers !