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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 A1, B1, and C1 be the centers of these equilateral triangles. Prove that the points A1, B1, and C1 form an equilateral triangle, which is known as the outer Napoleon triangle of triangle ABC.

Napoleon's theorem I

Problem 246

Napoleon's Theorem,
Triangles, equilateral,
Geometry joy.

Three triangles formed,
Outer Napoleon unveiled,
Geometry thrives.

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See also:

Problem 1205: Triangle, Centroid, Outer and Inner Napoleon Equilateral Triangles.

Problem 247: Napoleon's Theorem II. Internal Equilateral triangles. Inner triangle
Problem 248: Napoleon's Theorem III. Area Inner and Outer Napoleon triangles

iPad Apps: Apollonius: Napoleon's Theorem. External Equilateral Triangles


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