Question 23
Isosceles $\triangle ABC$ has a right angle at $C.$ Point $P$ is inside $\triangle ABC,$ such that $PA = 11,$ $PB = 7,$ and $PC = 6.$ Legs $\overline{AC}$ and $\overline{BC}$ have length $s = \sqrt{a + b\sqrt{2}},$ where $a$ and $b$ are positive integers. What is $a + b?$
