Question 91
Let triangle $ABC$ be such that $AB = AC = 22$ and $BC = 11$. Point $D$ is chosen in the interior of the triangle such that $AD = 19$ and $\angle ABD + \angle ACD = 90^\circ$. The value of $BD^2 + CD^2$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100a + b$.