# Solution to the Three Overlapping Circles Puzzle +-- {.image} [[ThreeOverlappingCircles.png:pic]] > What's the total shaded area? =-- ## Solution by [[Dissection]] and [[Circle Area]] +-- {.image} [[ThreeOverlappingCirclesLabelled.png:pic]] =-- It was noted in the twitter thread that the centres of each circle lie at the intersections of the other two. This means that the radii of the circles is $4$. Consider the blue region with vertices $A$, $B$, and $C$. The curved area below the line segment $A B$ is [[congruent]] to the purple shaded region, meaning that the blue region has the same area as the region outlined in green. This is a sector with central angle $60^\circ$ and radius $4$. Taking three of them gives a semi-circle so has area $\frac{1}{2} \pi 4^2 = 8 \pi$.