Let ABC be an acute triangle with AC>AB. Let Γ be the circle circumscribed to the triangle ABC and D the midpoint of the smaller arc BC of this circle. Let I be the incenter of ABC and let E and F be points on sides AB and AC, respectively, such that AE=AF and I lies on the segment EF. Let P be the second intersection point of the circumcircle of the triangle AEF with Γ with P=A. Let G and H be the intersection points of the lines PE and PF with Γ different from P, respectively. Let J and K be the intersection points of lines DG and DH with lines AB and AC, respectively. Show that the line JK passes through the midpoint of BC. geometryincentercircumcircle