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integer right triangles with M inside such that MA, MB, MC integers also

Source: 2017 XX All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p4

May 6, 2021
Integersright trianglegeometryUkrainian TYM

Problem Statement

Specify at least one right triangle ABCABC with integer sides, inside which you can specify a point MM such that the lengths of the segments MA,MB,MCMA, MB, MC are integers. Are there many such triangles, none of which are are similar?
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