Question 62
The bisectors of $\angle A$, $\angle B$ and $\angle C$ of $\triangle ABC$ meet its circumcircle at points $A_1$, $B_1$ and $C_1$, respectively. Set $AA_1 \cap CC_1 = I$, $AA_1 \cap BC = N$ and $BB_1 \cap A_1C_1 = P$. Denote by $O$ the circumcenter of $\triangle IPC_1$ and let $OP \cap BC = M$. If $BM = MN$ and $\angle BAC = 2 \angle ABC$, find the angles of $\triangle ABC$.