“…Take the lines through a, c, e parallel to the segments ce, ea, ac, respectively, the intersection points of these lines are denoted by a * , c * , e * (they are opposite to a, c, e, respectively, as shown in Figs. [1][2][3][4]. From the maximality of the area of T we conclude that the straight lines through the vertices parallel to the opposite sides of T are supporting lines of H. Therefore we know that b ∈ ae * c, d ∈ ca * e, and f ∈ ac * e. Case 1. f = f 0 .…”