Problem

Source: ELMO Shortlist 2024 G8

Tags: geometry, ellipse, conics, ELMO Shortlist



Let ABC be a triangle, and let D be a point on the internal angle bisector of BAC. Let x be the ellipse with foci B and C passing through D, y be the ellipse with foci A and C passing through D, and z be the ellipse with foci A and B passing through D. Ellipses x and z intersect at distinct points D and E, and ellipses x and y intersect at distinct points D and F. Prove that AD bisects angle EAF. Andrew Carratu