Consider a triangle ABC and construct its orthocenter D (intersection of altitudes). Then, create a circumcircle d through points B, C and D and two lines through D parallels to the sides b and c respectivelly. Take E and F to be the intersection points of these parallel lines with circle d and consider triangle DEF.[br]Ask about relations between segments AB and DE. [br][br]This example appears as example 179 in: Chou, S.C.: Mechanical geometry theorem proving, Mathematics and its Applications, vol. 41. D. Reidel Publishing Co., Dordrecht (1988)[br]

What about segments AC and DF?[br]And... What about segments BC and EF?