M is the midpoint of BC,

∴CD=DN，

AP/PM=AN/ND=AN/(NC/2)=2AN/NC=4，

∴AP=4PM.

Solution 2 M is the midpoint of BC,

∴ vector AM=(AB+AC)/2,

B, p, n three-point * * * line, AN=2NC,

∴ vector AP = xab+(1-x) an = xab+(2/3) (1-x) AC,

AP∑AM, AB, AC lines,

∴x=(2/3)( 1-x),3x=2-2x,x=2/5，

∴AP=(4/5)AM，

∴AP=4PM.