# Three circles, one triangle and a pink area

Geometry Level 4

We have an equilateral triangle of side $$a$$ (its height will be labelled as $$h$$). If each side's midpoint is a circumcentre for a circle of radius $$\frac{1}{3}h$$, find the triangle's area that is not overlapped by any of the circles (pink area on the image below).

If $$m, n$$ are both positive integers, then the area can be presented as: $$\frac{m\sqrt{3} - \pi}{n} a^{2}$$

Submit answer as: $$|m - n|$$

Note: keep in mind that this image is done in paint, therefore it is very inaccurate.

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