MathDB
Right-angled triangle

Source: 239 Open MO 2018, Junior League, Problem 2

April 4, 2023
geometry

Problem Statement

On the hypotenuse ABAB of a right-angled triangle ABCABC, point RR is chosen, on the cathetus BCBC a point TT, and on the segment ATAT a point SS are chosen in such a way that the angles ART\angle ART and ASC\angle ASC are right angles. Points MM and NN are the midpoints of the segments CBCB and CRCR, respectively. Prove that points MM, TT, SS, and NN lie on the same circle.
Proposed by S. Berlov