Very interesting, a pyramid and sphere inscribed

JuanR
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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}
 
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* 180^{o} means 180 degree
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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