Problem

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

Tags: geometry



The inscribed circle of $\Delta ABC$ is tangent to $AC$ and $BC$ in points $M$ and $N$ respectively. Line $MN$ intersects line $AB$ in point $P$, so that $B$ is between $A$ and $P$. Determine $\angle ABC$, if $BP=CM$.