Geometry Problem: Machu Picchu Inca Trail

 Problem 262. Regular Hexagon inscribed in a circle, sum of distances

The figure shows a regular hexagon ABDEF inscribed in a circle. If point G is on arc BC, GA = a, GB = b, GC = c,
GD = d, GE = e, GF = f, prove that a + b + c d = e + f.

Problem 262: Regular hexagon inscribed
 

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
  Equilateral Triangle

Regular hexagon inscribed in a circle

 

 

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