# Looks like an spherical square in the middle

Geometry Level 5

A disc of radius 1 unit is cut into 4 quadrants. These are placed in a square of side 1 unit (these quadrants do not have any part outside the square). What is the least possible area of overlap shared by all quadrants?

If this area can be written as $$\dfrac {a+b\sqrt{c}+d\pi}{e}$$, where $$a$$, $$b$$, $$c$$ $$d$$ and $$e$$ are integers, with $$c$$ and $$e$$ being positive, $$c$$ being square-free and $$\gcd(a,b,d,e)=1$$, find $$abcde$$.

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