# Crazy circles

Geometry Level 5

Three circles mutually tangent with centers $$A$$, $$B$$ and $$C$$ have radii of $$21$$, $$14$$ and $$c$$ respectively. Let the circle with center $$D$$ and radius $$2$$ be internally tangent to the three circles, and let the circle with center $$E$$ and radius $$R$$ be externally tangent to the three circles. Find $$\lfloor 100(c+R) \rfloor$$.

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