Let scalene triangle ABC have orthocentre H and circumcircle Γ. AH meets Γ at D distinct from A. BH and CH meet CA and AB at E and F respectively, and EF meets BC at P. The tangents to Γ at B and C meet at T. Show that AP and DT are concurrent on the circumcircle of AFE. concurrencyconcurrentorthocentercircumcirclegeometry