Semicircle \Gamma has diameter \overline{A B} of length 14. Circle \Omega lies tangent to \overline{A B} at a point P and intersects \Gamma at points Q and R. If Q R=3 \sqrt{3} and \angle Q P R=60^{\circ}, then the area of \triangle P Q R 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 ?
Answer Choices
A. 110
B. 114
C. 118
D. 122
E. 126