Albanian IMO TST 2010 Question 5
Source:
May 22, 2010
geometry3D geometryspherecombinatorics unsolvedcombinatorics
Problem Statement
a) Let's consider a finite number of big circles of a sphere that do not pass all from a point. Show that there exists such a point that is found only in two of the circles. (With big circle we understand the circles with radius equal to the radius of the sphere.)
b) Using the result of part show that, for a set of points in a plane, that are not all in a line, there exists a line that passes through only two points of the given set.