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 A_{1}B_{1}C_{1}
is the
outer Napoleon triangle of area S_{1} and A_{2}B_{2}C_{2}
is the
inner Napoleon triangle of area S_{2}, prove that S = S_{1} 
S_{2}.
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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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