Online Geometry, Theorems and Problems

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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