Question 91
Let $ABC$ be a triangle whose longest side is $BC$, and the angle $\angle BCA$ is three times greater than $\angle ABC$. The exterior angle bisector at vertex $A$ meets the line $BC$ at point $A_0$, and the exterior angle bisector at vertex $B$ meets the line $AC$ at point $B_0$. If $|AA_0| = |BB_0|$, determine the angles of the given triangle.
