Total Areas of Alternating Subtriangles in a Regular Polygon with 2n Sides

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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.


Drag the point P to change the figure.


Contributed by: Jay Warendorff (January 2009)
Open content licensed under CC BY-NC-SA



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

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