Geometry Problem 246. Napoleon's Theorem I. External Equilateral triangles. Outer triangle. Online High School, College, SAT Prep.

In the figure, equilateral triangles ABC', BCA', and ACB' are constructed externally on the sides of a triangle ABC. Prove that the centers A₁, B₁, and C₁ of those equilateral triangles form an equilateral triangle, called the outer Napoleon triangle. View or post a solution.

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