Problem

A_1, A_2, A_3, \dots, A_n

is a regular polygon of

n

sides circumscribed about a circle of centre

O

and radius '

a

P

is any point distant '

c

' from

O

. Show that the sum of the squares of the perpendiculars from

P

on the sides of the polygon is

n \left( a^2 + \frac{c^2}{2} \right)