Since MP is perpendicular to AC, it follows:
angle AMP=angle CMP = 90°
let's call angle MPC=m
and also angle MCP = t
since AB=AC the triangle ABC is isosceles, thus
angle B = angle MCP = t
Finally, call APB= p
Since the angles forming a straight line must sum 180°, it follows that:
P + 90° - m + m = 180°
Simplifying:
P = 90°
Triangle ABP is right in P
This makes that m = 90 - m
and m=45°
Finally, since t = P - m
t = 45°
It follows that
angle APB = 2 ¨* angle B
