Let D be an interior point on the side BC of an acute-angled triangle ABC. Let the circumcircle of triangle ADB intersect AC again at E(=A) and the circumcircle of triangle ADC intersect AB again at F(=A). Let AD, BE, and CF intersect the circumcircle of triangle ABC again at D1(=A), E1(=B) and F1(=C), respectively. Let I and I1 be the incentres of triangles DEF and D1E1F1, respectively. Prove that E,F,I,I1 are concyclic. geometryincentercircumcircleINMO 2022