LP bisects BD
Source: I Soros Olympiad 1994-95 Round 2 10.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
May 25, 2024
geometrybisect
Problem Statement
A circle can be drawn around the quadrilateral . Let straight lines and intersect at point , and straight lines and intersect at point . (Points and lie on segments and , respectively.) Let be the projection of point onto straight line , be the projection of point on the straight line . Prove that the straight line divides the diagonal in half.