We've got a tetrahedron ABCD, in which the BCA = BAD,

a sphere with center S appended to this tetrahedron is tangent to the wall

ABC in the middle of the circle described on this wall. To prove that a straight lines

AD and AS are perpendicular.

(Note: The sphere appended to the tetrahedron is the sphere tangent to exactly

one wall and the other three planes containing the wall.)