Problem

Source: 2020 Kazakhstan MO grades X P3, XI P3

Tags: geometry, equal segments, equal angles



A point N is marked on the median CM of the triangle ABC so that MNMC=AB2/4. Lines AN and BN intersect the circumcircle ABC for the second time at points P and Q, respectively. R is the point of segment PQ, nearest to Q, such that NRC=BNC. S is the point of the segment PQ closest to P such that NSC=ANC. Prove that RN=SN.