MathDB

A line

g

is given in a plane.

n

distinct points are chosen arbitrarily from

g

and are named as

A_1, A_2, \ldots, A_n

. For each pair of points

A_i,A_j

, a semicircle is drawn with

A_i

and

A_j

as its endpoints. All semicircles lie on the same side of

g

. Determine the maximum number of points (which are not lying in

g

) of intersection of semicircles as a function of

n

Problem Statement