Problem 248. Napoleon's Theorem III. Area Inner and outer Napoleon triangles. Online High School, College.

The figure shows a triangle ABC of area S. If A₁B₁C₁ is the outer Napoleon triangle of area S₁ and A₂B₂C₂ is the inner Napoleon triangle of area S₂, prove that S = S₁ - S₂.
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Napoleon Theorem III Inner and Outer triangles

See also:
Problem 1205: Triangle, Centroid, Outer and Inner Napoleon Equilateral Triangles.
Problem 246: Napoleon's Theorem I. External Equilateral triangles. Outer triangle
Problem 247: Napoleon's Theorem II. Internal Equilateral triangles. Inner triangle
iPad Apps: Apollonius: Napoleon's Theorem. External Equilateral Triangles.

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