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construction of 3 points on sides of an acute triangle

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P9

August 2, 2018
geometryconstruction

Problem Statement

Let ABCABC be an acute-angled triangle. Construct points A′,B′,C′A', B', C' on its sides BC,CA,ABBC, CA, AB such that: - A′B′∥ABA'B' \parallel AB, - C′CC'C is the bisector of angle A′C′B′A'C'B', - A′C′+B′C′=ABA'C' + B'C'= AB.
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