Problem

Source: JBMO 2021

Tags: Junior, Balkan, geometry, circumcircle, concurrence



Let ABC be an acute scalene triangle with circumcenter O. Let D be the foot of the altitude from A to the side BC. The lines BC and AO intersect at E. Let s be the line through E perpendicular to AO. The line s intersects AB and AC at K and L, respectively. Denote by ω the circumcircle of triangle AKL. Line AD intersects ω again at X. Prove that ω and the circumcircles of triangles ABC and DEX have a common point.