MathDB

Given is a pyramid

SABCD

whose base is a convex quadrilateral

ABCD

with perpendicular diagonals

AC

and

BD

, and the orthogonal projection of vertex

S

onto the base is the point

0

of the intersection of the diagonals of the base. Prove that the orthogonal projections of point

O

onto the lateral faces of the pyramid lie on the circle.

Problem Statement