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moving two triangles with 1 angle a, to construct angle a/2

Source: Sharygin Geometry Olympiad 2015 Final 8.5

August 1, 2018
geometrybisectionangle bisector

Problem Statement

Two equal hard triangles are given. One of their angles is equal to α \alpha (these angles are marked). Dispose these triangles on the plane in such a way that the angle formed by some three vertices would be equal to α/2 \alpha / 2. (No instruments are allowed, even a pencil.)
(E. Bakayev, A. Zaslavsky)