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

Tags were heavily modified to better represent problems.

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Found problems: 52

1947 Moscow Mathematical Olympiad, 127
Tags: equal circles , circles , geometry , circumcircle
Point $O$ is the intersection point of the heights of an acute triangle $\vartriangle ABC$. Prove that the three circles which pass: a) through $O, A, B$, b) through $O, B, C$, and c) through $O, C, A$, are equal

1956 Poland - Second Round, 2
Tags: geometry , equal circles , orthocenter
Prove that if $ H $ is the point of intersection of the altitudes of a non-right triangle $ ABC $, then the circumcircles of the triangles $ AHB $, $ BHC $, $ CHA $ and $ ABC $ are equal.