Problem

A polygon of

n

sides, inscribed in a circle, is such that its sides subtend angles

2\alpha, 4\alpha, \dots, 2n\alpha

at the centre of the circles. Prove that its area

A_1

, is to the area

A_2

of the regular polygon of

n

sides inscribed in the same circle, as

\sin n\alpha : n \sin \alpha