A circle is inscribed in a quadrilateral $ABCD$ ($M$ and $N$ are points of tangency with $AD$ and $BC$),$AC$ intersects $MN$ at $P$, such that $CP=10$, $CN=8$ and $AM=4$.Calculate $AP$. (S:$AP=5$)
I made the drawing but I can only determine the values $CE=8$, $AF=4$. $4+BF+DE+8=4+DM+8+BN⟹BF+DE=BN+DM$
