Recall that a regular polygon is one with all sides of equal length and all internal angles equal. A polygon with n sides is often referred to as an n-gon.* In what follows, suppose A1 A2 ... An is a regular n-gon in the Euclidean plane for some n > 3. 1. Let li, l2, ... , and ln be the lines bisecting (i.e. cutting in half) the interior angles at A1, A2, ... , and An, respectively, of the regular n-gon A1 A2 ... An. Show that li, l2, ... , and ln are concurrent, that is meet at a common point 0. [4] 2. Let mi, m2, ..., and mn be the perpendicular bisectors (i.e. lines cutting in half at a right angle) of the sides A1 A2, A2A3, ... , and An A1, respectively, of the regular n-gon A1 A2 ... An. Show that mı, m2, ... , and mn are concurrent also concurrent at the point O in question 1. [4] 3. Besides the regular polygon A1 A2 ... An, what else is the point O a centre of? [2]