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Part of 2009 IberoAmerican Olympiad For University Students

Problems(1)

Triangle cut in similar triangles - OIMU 2009 Problem 1

Source:

A line through a vertex of a non-degenerate triangle cuts it in two similar triangles with

\sqrt{3}

as the ratio between correspondent sides. Find the angles of the given triangle.

ratiogeometrysimilar trianglesgeometry proposed