Similar triangles problem

Hello everyone! This is my first post on MHF.
Can anybody help me solving this problem applying the properties of similar triangles?

I know the answer is "2" but can't figure out how to get the result.

It goes like this:
"Let ABC be a right angled triangle such that the angle A = 90 degrees, AB = AC and let M be the mid point of the side AC. Take the point P on the side BC so that AP is vertical to BM. Let H be the intersection point of AP and BM.

1)Find the ratio of the areas of the two triangles ABH : AHM (I did this one)
2) Find the ratio BP : PC (This is the one I want to solve)"

Thank you!

Hint :



Attachment 23822