I got 2 math problems can you help me ?

1. Suppose that a sphere of radius 1 is inscribed in a right circular cone with radius r and height h.

(1) Express r in terms of h !

(2) Find the minimum of the volume of such a right circular one !

2.Let Triangle ABC be a right angled such that

, 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

!

(2) Find the ratio BP : PC !

Thanks for your attention