Isosceles \triangle A B C has a right angle at C. Point P is inside \triangle A B C, such that P A=11, P B=7, and P C=6. Legs \overline{A C} and \overline{B C} have length s=\sqrt{a+b \sqrt{2}}, where a and b are positive integers. What is a+b ?
Answer Choices
A. 85
B. 91
C. 108
D. 121
E. 127