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.
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A generalization of problem 4.28 in Problems in Plane and Solid Geometry v.1 Plane Geometry by Viktor Prasolov.
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