Three circles are drawn tangentially to each other, their centres collinear as shown. The line $AB$ is tangential to the two smaller circles and is 8 units long.

Philip Morgan, age 17, Judd School, Tonbridge, Kent, Zoe Hayward, age 16, Outwood Grange School, Wakefield and Sue Liu of Madras College, St Andrews and Katharina Jurges, age 17, of the Lycee International des Pontonniers, Strasbourg, France sent solutions. Well done!

Let the radius of the big circle equal $a$, the radius of the medium circle equal $b$ and the radius of the smallest circle equal $c$. Considering the diameter of the big circle: $2a = 2b + 2c$, so $a = b + c$.

Let the centre of the larger circle be $O$ and the point where the chord touches the smaller circles be $D$.

Construct the right-angled triangle $AOD$. Now, by Pythagoras' Theorem,

$AO^2 = OD^2 + DA^2$

$(b + c)^2 = (b - c)^2 + 4^2$

$bc = 4$

The area needed is $\pi(b + c)^2 - \pi b^2 - \pi c^2 = 2\pi bc = 8\pi$.