Show that if 2n points are marked on the circumference of a

Show that if 2n points are marked on the circumference of a circle and if a_n is the number of ways of joining them in pairs by n non-intersecting chords, then a_n = C_n.

Solution

Let there are 2n points on the circle

there are 2nCn ways to select any n points from the 2n points but due to symmetry of the circle it will be divided by (n+1) because of repeatition.

Catalan number = Cn = (2nCn)/(n+1)

So an=Cn