Question 153
Let $ABC$ be a triangle with $\angle B = 2\angle C$ and angle bisector $BD$. The symmedian of vertex $B$ in triangles $DAB$, $BCD$ cuts the corresponding circumcircle at $M$, $N$. Denote $P$ as the reflection of $B$ over $C$. Prove that the circle $(MNP)$ is tangent to $BC$ and both of circles $(DAB), (BCD)$.