MathDB
n points lie on a circle, no three chords are concurrent

Source: Greece JBMO TST 2013 p2

April 29, 2019
combinatoricscombinatorial geometrycircleChordsconcurrent

Problem Statement

Consider nn different points lying on a circle, such that there are not three chords defined by that point that pass through the same interior point of the circle. a) Find the value of nn, if the numbers of triangles that are defined using 33 of the n points is equal to 2n2n b) Find the value of nn, if the numbers of the intersection points of the chords that are interior to the circle is equal to 5n5n.