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Geometry Problem 1205: Triangle, Centroid, Outer and Inner Napoleon Equilateral Triangles. Online High School, College.

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In the figure, G is the centroid of a triangle ABC. If A1B1C1 and A2B2C2 are the outer and the inner Napoleon triangles of triangle ABC, prove that G is the centroid of triangles A1B1C1 and A2B2C2.
  

Geometry Problem 1205: Triangle, Centroid, Outer and Inner Napoleon equilateral triangles.
  

See also:
Problem 246: Napoleon's Theorem I. External Equilateral triangles. Outer triangle

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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Last updated: Apr 9, 2016