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intersecting squares, black triangle area equals to sum of gray areas

Source: 2017 Oral Moscow Geometry Olympiad grades 8-9 p5

July 26, 2019
geometrySquaresareas

Problem Statement

Two squares are arranged as shown. Prove that the area of the black triangle equal to the sum of the gray areas. https://2.bp.blogspot.com/-byhWqNr1ras/XTq-NWusg2I/AAAAAAAAKZA/1sxEZ751v_Evx1ij7K_CGiuZYqCjhm-mQCK4BGAYYCw/s400/Oral%2BSharygin%2B2017%2B8.9%2Bp5.png