MathDB

2017.4

Part of Ukrainian TYM Qualifying - geometry

Problems(1)

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

5/6/2021
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?
Integersright trianglegeometryUkrainian TYM