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Romanian District Olympiad 2015, Grade VII, Problem 4

Source:

September 25, 2018
geometrycenter of gravity

Problem Statement

At the exterior of the square ABCD ABCD it is constructed the isosceles triangle ABE ABE with ∠ABE=120∘.M \angle ABE=120^{\circ} . M is the intersection of the bisector line of the angle ∠EAB \angle EAB with its perpendicular that passes through B;N B; N is the intersection of the AB AB with its perpendicular that passe through M;P M; P is the intersection of CN CN with MB. MB. If G G is the center of gravity of the triangle ABE, ABE, prove that PG PG and AE AE are parallel.
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