Question 46
The incircle of $\triangle ABC$ touches the sides $BC$ and $AC$ at points $A_1$ and $B_1$, respectively. The lines $B_1A_1$ and $AB$ are concurrent at $X$ such that $A$ lies between $X$ and $B$. If $\angle CXB = 90^\circ$ and $BC^2 = AB^2 + BC \cdot AC$ find the angles of $\triangle ABC$.
