Geometry Problem: Machu Picchu Inca Trail

Problem 248. Napoleon's Theorem III. Area Inner and outer Napoleon triangles

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.

Napoleon Theorem III Inner and Outer triangles 

See also: 

  Problem 247
  Problem 246
  Equilateral Triangle

Napoleon Theorem and Problem Index

 

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