intersection of (BPK), (DQK) lies on diagonal BD of trapezoid ABCD
Source: VI Soros Olympiad 1990-00 R1 9.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
May 27, 2024
geometrytrapezoidconcurrencyConcyclic
Problem Statement
A straight line is drawn through an arbitrary internal point of the trapezoid , intersecting the bases of and at points and , respectively. The circles circumscribed around the triangles and intersect, besides the point , also at the point . Prove that the point lies on the diagonal .