Let ABC be an acute triangle and Γ its circumcircle. The lines tangent to Γ through B and C meet at P. Let M be a point on the arc AC that does not contain B such that M=A and M=C, and K be the point where the lines BC and AM meet. Let R be the point symmetrical to P with respect to the line AM and Q the point of intersection of lines RA and PM. Let J be the midpoint of BC and L be the intersection point of the line PJ and the line through A parallel to PR. Prove that L,J,A,Q, and K all lie on a circle. geometrycircumcircleIberoamericanIberoamerican 2016