Three acute inscribed triangles determine a nonobtuse one
Source: XII Cono Sur Mathematical Olympiad (2001)
July 28, 2011
geometryrectanglecombinatorics unsolvedcombinatorics
Problem Statement
Three acute triangles are inscribed in the same circle with their vertices being nine distinct points. Show that one can choose a vertex from each triangle so that the three chosen points determine a triangle each of whose angles is at most .