Geometry value putting trick

In an isosceles triangle ABC a circle passes through vertex B and touches mid-point of line AC at Q and intersects the side AB at P. Find AP: PB?

or it can be asked in this manner

ABC is an isosceles triangle in which AB = AC. A circle through B touches the side AC at D and intersect the side AB at P. If D is the midpoint of side AC, Then  Prove  AB = 4 AP.