MathDB
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 ABCDABCD. Let straight lines ABAB and CDCD intersect at point MM, and straight lines BCBC and ADAD intersect at point KK. (Points BB and PP lie on segments AMAM and AKAK, respectively.) Let PP be the projection of point MM onto straight line AKAK, LL be the projection of point KK on the straight line AMAM. Prove that the straight line LPLP divides the diagonal BDBD in half.