Let ABC be an acute triangle with AC>AB. be Γ the circumcircle circumscribed to the triangle ABC and D the midpoint of the smallest arc BC of this circle. Let E and F points of the segments AB and AC respectively such that AE=AF. Let P=A be the second intersection point of the circumcircle circumscribed to AEF with Γ. Let G and H be the intersections of lines PE and PF with Γ other than P, respectively. Let J and K be the intersection points of lines DG and DH with lines AB and AC respectively. Show that the JK line passes through the midpoint of BC geometrymidpointintersectionscircumcirclearc midpoint