collinearity wanted, sphere and pyramid
Source: All - Russian Regional Olympiad (Round 4) 1993 11.3
August 26, 2024
geometry3D geometryspherepyramid
Problem Statement
Point is the foot of the altitude of a quadrilateral pyramid. A sphere with center is tangent to all lateral faces of the pyramid. Points are taken on successive lateral edges so that segments , , and pass through the three corresponding tangency points of the sphere with the faces. Prove that the segment passes through the fourth tangency point