Intermission

Geometry Level pending

An triangle with sides 529 (red) and 128 (cyan) is inscribed in a circle (purple) of diameter 721. The length of the remaining longest side (black) in its simplest form can be represented as $$\frac{1}{721}\sqrt{a+b\sqrt{c}}$$ where $$a,b$$ and $$c$$ are positive integers. Find $$a+b+c$$.

×