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sum of areas among semicircles, with diameters sides of right triangle

Source: 1989 Chile NMO p3

September 5, 2022
geometryareasright trianglesemicircle

Problem Statement

In a right triangle with legs aa, bb and hypotenuse cc, draw semicircles with diameters on the sides of the triangle as indicated in the figure. The purple areas have values X,YX,Y . Calculate X+YX + Y. https://cdn.artofproblemsolving.com/attachments/1/a/5086dc7172516b0a986ef1af192c15eba4d6fc.png
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