Napoleon's Theorem states that if you construct an equilateral triangle on the the outside of each side of any existing triangle, then connect the centers of those three new triangles, you will form another equilateral triangle, known as the Outer Napoleon Triangle. Similarly, the Inner Napoleon Triangle, which connects the centers of equilateral triangles formed on the insides of each side of a triangle, is also equilateral.
Construct an Outer Napoleon Triangle. In the plot below, add 3 points to define the initial triangle. Then, click "Add exterior triangles" to construct the 3 equilateral triangles on the outside of your original figure. Finally, click "Add Napoleon Triangle" to construct the triangle formed by connecting the center points of the 3 equilateral triangles.
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