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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.
 

Quadrilateral, Diagonals, Incenters, Metric Relations
 

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