Let △ABC be a triangle with orthocenter H and altitudes AD, BE and CF. Let D′, E′ and F′ be the intersections of the heights AD, BE and CF, respectively, with the circumcircle of △ABC, so that they are different points from the vertices of triangle △ABC. Let L, M and N be the midpoints of BC, AC and AB, respectively. Let P, Q and R be the intersections of the circumcircle with LH, MH and NH, respectively, such that P and A are on opposite sides of BC, Q and A are on opposite sides of AC and R and C are on opposite sides of AB. Show that there exists a triangle whose sides have the lengths of the segments D′P, E′Q, and F′R. triangle inequalitygeometryaltitudes