Total Areas of Alternating Subtriangles in a Regular Polygon with 2n Sides
Let P be a point connected to and inside the vertices of a polygon with sides. Number the triangles counterclockwise from to . Then the sum of the areas of the even-numbered triangles is equal to the sum of the areas of the odd-numbered triangles.[more]
Drag the point P to change the figure.[less]
A generalization of problem 4.28 in Problems in Plane and Solid Geometry v.1 Plane Geometry by Viktor Prasolov.