China Western Mathematical Olympiad

In $△ABC$, $AB=AC$, the inscribed circle $I$ touches $BC$, $CA$, $AB$ at points $D$, $E$ and $F$ respectively. $P$ is a point on arc $\widehat{EF}$ (not containing $D$). Line $BP$ intersects the circle $I$ at another point $Q$, and lines $EP$, $EQ$ meet line $BC$ at $M$, $N$ respectively. Prove that

(1) $P$, $F$, $B$, $M$ are concyclic;

$$(2)\frac{EM}{EN}=\frac{BD}{BP}.$$