Definition:Polar Triangle

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Let $\triangle ABC$ be a spherical triangle on the surface of a sphere whose center is $O$.

Let the sides $a, b, c$ of $\triangle ABC$ be measured by the angles subtended at $O$, where $a, b, c$ are opposite $A, B, C$ respectively.

Let $A'$, $B'$ and $C'$ be the poles of the sides $BC$, $AC$ and $AB$ respectively which are in the same hemisphere as the points $A$, $B$ and $C$ respectively.


Then the spherical triangle $\triangle A'B'C'$ is the polar triangle of $\triangle ABC$.

Also see

  • Results about polar triangles can be found here.