Hans Walser, [20110221a]

Area of Stars

The black points are the vertices of a regular n-gon. The blue point (the center of the star on the right) is an arbitrary point on the circle through the black points.

Prove: The area of the left star is half the area of the star on the right.

What about the case ?

Fig. 1: n = 3

Fig. 2: n = 4

Fig. 3: n = 5