Two squares and a semicircle of diameter 4. What is the total square area?

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## Solution

The total square area is 4.

This solution takes a point on the diameter that is the left square side (a) to the left of the lower right vertex of the right square. From this point two right triangles can be constructed which, by comparing sides a and b and using SAS, are seen to be congruent.

So this point is equidistant from the circle circumference and on diameter and therefore^{1}The point is the intersection of the perpendicular bisector of the two circumference points and the diameter, and therefore it is unique. must be the circle centre. Using the Pythagorean theorem, one can calculate the sum of the square areas.

Please find here a beautiful animated solution including all possible configurations by Per Henrik Christiansen.

## Visual solution

## Poem

The elephant and the mouse

In this small house

The 2 went to a race

To see who would take the 1st place

The elephant was big and scared

The mouse small and well prepared

The race begun

What a fun !

The elephant hidden behind a tree so easy

So nice to see

The mouse won easily