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Romanian National Olympiad 2024 - Grade 10 - Problem 2

Source: Romanian National Olympiad 2024 - Grade 10 - Problem 2

April 6, 2024

geometrycircumcirclepentagoninscriptibleCentroid

Problem Statement

We consider the inscriptible pentagon

ABCDE

in which

AB=BC=CD

and the centroid of the pentagon coincides with the circumcenter. Prove that the pentagon

ABCDE

is regular.
The centroid of a pentagon is the point in the plane of the pentagon whose position vector is equal to the average of the position vectors of the vertices.

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