# Wasn't it easy to find an equilateral triangle's side

Geometry Level 4

$$ABC$$ is an equilateral triangle. $$DE$$ is the tangent to the inscribed circle with $$D$$ on $$AB$$ and $$E$$ on $$AC$$. It is given that $$DE$$ perpendicular to $$AC$$ and $$AE=10$$.The side length of $$ABC$$ can be expressed as $$a+b\sqrt{c}$$ where $$a$$ and $$b$$ are positive integers and $$c$$ is square-free positive integer; then find $$a+b+c$$.

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