MathDB
Construction of a right triangle

Source: Czech and Slovak Olympiad 1965, National Round, Problem 2

June 24, 2024
ratiogeometrygeometric constructionright triangleconstruction

Problem Statement

Line segment AM=d>0AM=d>0 is given in the plane. Furthermore, a positive number vv is given. Construct a right triangle ABCABC with hypotenuse ABAB, altitude to the hypotenuse of the length vv and the leg BCBC being divided by MM in ration MB/MC=2/3MB/MC=2/3. Discuss conditions of solvability in terms of d,vd, v.