Geometry, Theorems and Problems

 Problem 261. Regular Pentagon inscribed in a circle, sum of distances

The figure shows a regular pentagon ABDE inscribed in a circle. If point F is on arc BC, prove that a + d = b + c + e.
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Regular pentagon fact
 

Geometry software that can be used to learn and research:

Geometry Expressions, Cabri, Cinderella, GeoGebra, Geometer Sketchpad, C.a.R., TracenPoche, Mathematica.

See also:
 

  Ptolemy's Theorem
  Pentagons

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