# Kick that altitude

Geometry Level 4

$$ABC$$ is an acute triangle with an area of $$18$$. Let $$P$$ be the foot of the perpendicular from $$A$$ to $$BC$$ and let $$Q$$ be the foot of the perpendicular from $$C$$ to $$AB$$. The area of the triangle $$BPQ$$ is $$2,$$ and the length of $$PQ$$ is $$2\sqrt{2}.$$

Let $$\Gamma$$ be the circumcircle of $$ABC$$. The radius of $$\Gamma$$ can be written as $$\frac{a}{b},$$ where $$a$$ and $$b$$ are coprime positive integers. Find $$a+b.$$

×