# Hard, pyramid and sphere inscribed

• October 4th 2007, 10:09 AM
Ununuquantium
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 $\angle APB + \angle CPD = 180^{o}$
• October 9th 2007, 06:44 AM
Ununuquantium
Can anybody tell me what are the conditions to inscribe sphere in a such pyramid
• October 17th 2007, 08:02 AM
terafull
I remember that base must be circonscrit on a circle. Can anyone confirm?