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: 53

2015 Costa Rica - Final Round, G1
Tags: equilateral , arc , geometry
Points $A, B, C$ are vertices of an equilateral triangle inscribed in a circle. Point $D$ lies on the shorter arc $\overarc {AB}$ . Prove that $AD + BD = DC$.

1940 Moscow Mathematical Olympiad, 063
Tags: equilateral , arc , geometry
Points $A, B, C$ are vertices of an equilateral triangle inscribed in a circle. Point $D$ lies on the shorter arc $\overarc {AB}$ . Prove that $AD + BD = DC$.

2006 Sharygin Geometry Olympiad, 8.4
Tags: bisects , arc midpoint , arc , equal circles , geometry
Two equal circles intersect at points $A$ and $B$. $P$ is the point of one of the circles that is different from $A$ and $B, X$ and $Y$ are the second intersection points of the lines of $PA, PB$ with the other circle. Prove that the line passing through $P$ and perpendicular to $AB$ divides one of the arcs $XY$ in half.