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right triangle out of an interior point of an equilateral

Source: Nordic Mathematical Contest 2003 #3

September 24, 2017

Equilateral Triangleright trianglesgeometry

Problem Statement

The point

{D}

inside the equilateral triangle

{\triangle ABC}

satisfies

{\angle ADC = 150^o}

. Prove that a triangle with side lengths

{|AD|, |BD|, |CD|}

is necessarily a right-angled triangle.