3
Part of 1980 Bundeswettbewerb Mathematik
Problems(2)
2n+3 points in the plane
Source:
11/8/2003
Given 2n+3 points in the plane, no three on a line and no four on a circle, prove that it is always possible to find a circle C that goes through three of the given points and splits the other 2n in half, that is, has n on the inside and n on the outside.
combinatorial geometrycombinatorics solvedcombinatorics
Bundeswettbewerb Mathematik 1980 Problem 2.3
Source: Bundeswettbewerb Mathematik 1980 Round 2
9/23/2022
In a triangle , points and distinct from the vertices of the triangle are chosen on sides and , respectively. The circumcircles of the triangles , , and are drawn. Prove that the centers of these circles are the vertices of a triangle similar to triangle .
geometryTrianglesimilarcircumcirle