Geometry Problem 246. Discover Napoleon's Theorem I: External Equilateral Triangles and Outer Triangle for High School,
and Math Education
Consider a triangle ABC. Construct equilateral triangles ABC', BCA', and ACB' externally on the sides of triangle ABC. Let A_{1}, B_{1}, and C_{1} be the centers of these equilateral triangles. Prove that the points A_{1}, B_{1}, and C_{1} form an equilateral triangle, which is known as the outer Napoleon triangle of triangle ABC.
Problem 246
Napoleon's Theorem,
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