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In the figure, G is the centroid of a triangle ABC. If A_{1}B_{1}C_{1} and A_{2}B_{2}C_{2} are the outer and the inner Napoleon triangles of triangle ABC, prove that G is the centroid of triangles A_{1}B_{1}C_{1} and A_{2}B_{2}C_{2}.

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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Post or view a solution to the problem 1205 Last updated: Apr 9, 2016