A Parallelogram Defined by the Centers of Four Incircles
Let ABC be a triangle. Let the line DEF be parallel to AC with D on AB and E on BC. Let the line FGH be parallel to AB with H on AC and G on BC. Let O, , , and be the incircles of the triangles ABC, DBE, FEG, and CGH, respectively. Then O is a parallelogram.
The statement of the theorem is in Problem 96. Similar Triangles, Incenters, Parallelogram.