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analogous triangles but not congruent

Source: Sharygin Final 2007 8.6

April 30, 2019
geometrycongruent trianglesequal angles

Problem Statement

Two non-congruent triangles are called analogous if they can be denoted as ABCABC and A′B′C′A'B'C' such that AB=A′B′,AC=A′C′AB = A'B', AC = A'C' and ∠B=∠B′\angle B = \angle B' . Do there exist three mutually analogous triangles?
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