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triangle construction given 3 points, one at each side

Source: 1986 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p3

November 21, 2022

geometryconstructionratio

Problem Statement

The points

S

lie on side

AB

T

on side

BC

, and

U

on side

CA

of a triangle so that the following applies:

\overline{AS} : \overline{SB} = 1 : 2

\overline{BT} : \overline{TC} = 2 : 3

and

\overline{CU} : \overline{UA} = 3 : 1

. Construct the triangle

ABC

if only the points

S, T

and

U

are given.