# Medial Ellipse?

Geometry Level 5

Given a 3-4-5 triangle $$ABC$$, find the area of the inscribed ellipse that is tangent to all three sides at their midpoints. If this area can be expressed as $$\frac{a\pi\sqrt{b}}{c}$$, where $$a$$, $$b$$ and $$c$$ are positive, $$\gcd(a,c)=1$$ and $$b$$ is square-free, find $$a+b+c$$.

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