Problem 582: Quadrilateral, Diagonals, Incenters, Metric Relations. Level: Mathematics Education, High School, SAT Prep, College
The figure shows a quadrilateral ABCD.
Diagonals AC and BD meet at O. If E, F, G, and H are the incenters of
triangles AOB, BOC, COD, and AOD, respectively, prove that EF2 +
GH2 = EH2 + FG2.
