Notes
circles around a triangle solution

Circles Around a Triangle

Solution by Dissection and Area of a Triangle

With the regions labelled as above, they combine as follows:

• $A + B + C$ and $D + E + F + G + H$ are large semi-circles, write this as $L$
• $D + J$ and $B + E + F$ are medium semi-circles, write this as $M$
• $H + I$ and $C + G + F$ are small semi-circles, write this as $S$
• $E + F + G$ is the triangle, write this as $T$

Then the shaded region can be expressed as follows:

As the triangle has side lengths $3$, $4$, and $5$ it is a right-angled triangle and has area $6$. So the shaded regions have total area $18$.