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integer side triangles, one inside another (2019 Kyiv City MO 10.3)

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September 16, 2020
geometryIntegersTriangles

Problem Statement

Call a right triangle ABCABC special if the lengths of its sides AB,BCAB, BC andCA CA are integers, and on each of these sides has some point XX (different from the vertices of △ABC \vartriangle ABC), for which the lengths of the segments AX,BXAX, BX and CXCX are integers numbers. Find at least one special triangle.
(Maria Rozhkova)
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