# Math Help - Hard, pyramid and sphere inscribed

1. ## Hard, pyramid and sphere inscribed

A pyramid $ABCDS$ is given (the base is convex quadrilateral). A sphere is inscribed in this pyramid and it is tangent to side $ABCD$ at point $P$.
Prove that $\angle APB + \angle CPD = 180^{o}$

2. Can anybody tell me what are the conditions to inscribe sphere in a such pyramid

3. I remember that base must be circonscrit on a circle. Can anyone confirm?