WOLFRAM|DEMONSTRATIONS PROJECT

The Eutrigon Theorem

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a
b
60°
a
b
c
Δ=Δ+Δ-Δ

The black central triangle with one angle equal to 60° is called a eutrigon. The areas of equilateral triangles constructed on the three faces
a
,
b
, and
c
obey the eutrigon theorem, which gives the area of the black triangle in terms of the areas of the other three triangles.