Right-angled triangle
Source: 239 Open MO 2018, Junior League, Problem 2
April 4, 2023
geometry
Problem Statement
On the hypotenuse of a right-angled triangle , point is chosen, on the cathetus a point , and on the segment a point are chosen in such a way that the angles and are right angles. Points and are the midpoints of the segments and , respectively. Prove that points , , , and lie on the same circle.Proposed by S. Berlov