The inscribed circle in $\triangle ABC$ touches $AB, BC, A$C respectively at $M, N, P$. How can I calculate the angles of $\triangle ABC$ if $\angle PNM:\angle PMN : \angle MPN = \angle BAC : \angle ACB : \angle ABC$.
Please only provide me with a hint. Thank you for understanding!
Hint: This condition means that triangles $\triangle ABC$ and $\triangle MNP$ are similar, and corresponding angles are equal.