Kick that altitude

Geometry Level 4

ABCABC is an acute triangle with an area of 1818. Let PP be the foot of the perpendicular from AA to BCBC and let QQ be the foot of the perpendicular from C C to ABAB. The area of the triangle BPQBPQ is 2,2, and the length of PQPQ is 22.2\sqrt{2}.

Let Γ \Gamma be the circumcircle of ABCABC. The radius of Γ\Gamma can be written as ab,\frac{a}{b}, where aa and bb are coprime positive integers. Find a+b.a+b.

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