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right triangle construction, given 3 points

Source: 2015 XVIII All-Ukrainian Tournament of Young Mathematicians named after M. Y. Yadrenko, Qualifying p21

May 7, 2021
geometryconstructionright triangleUkrainian TYM

Problem Statement

Let CHCH be the altitude of the triangle ABCABC drawn on the board, in which ∠C=90o\angle C = 90^o, CA≠CBCA \ne CB. The mathematics teacher drew the perpendicular bisectors of segmentsCA CA and CBCB, which cut the line CH at points KK and MM, respectively, and then erased the drawing, leaving only the points C,KC, K and MM on the board. Restore triangle ABCABC, using only a compass and a ruler.
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