Question 24
Semicircle $\Gamma$ has diameter $AB$ of length $14.$ Circle $\Omega$ lies tangent to $AB$ at a point $P$ and intersects $\Gamma$ at points $Q$ and $R.$ If $QR = 3\sqrt3$ and $\angle QPR = 60^\circ,$ then the area of $\triangle PQR$ is $\dfrac{a\sqrt b}{c},$ where $a$ and $c$ are relatively prime positive integers and $b$ is a positive integer not divisible by the square of any prime. What is $a + b + c?$