2020 IGO Intermediate P4
Source: 7th Iranian Geometry Olympiad (Intermediate) P4
November 4, 2020
geometryorthocenterIGO
Problem Statement
Triangle is given. An arbitrary circle with center , passing through and , intersects the sides and at and , respectively. Let be a point such that triangle is similar to triangle (with the same order) and the points and lie on the same side of the line . Similarly, let be a point such that triangle is similar to triangle (with the same order) and the points and lie on the same side of the line . Prove that the line passes through the orthocenter of the triangle .Proposed by Nguyen Van Linh - Vietnam