This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

1998 Junior Balkan Team Selection Tests - Romania, 2
We´re given an inscriptible quadrilateral $ DEFG $ having some vertices on the sides of a triangle $ ABC, $ and some vertices (at least one of them) coinciding with the vertices of the same triangle. Knowing that the lines $ DF $ and $ EG $ aren´t parallel, find the locus of their intersection. [i]Dan Brânzei[/i]
concyclic geometry pure geometry inscriptible

2024 Romania National Olympiad, 2
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. [i]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.[/i]
pentagon circumcircle geometry centroid inscriptible complex numbers