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Outer Inscribed Squares Triangle


TriangleSquareInscribing2

A similar construction can be done by initially erecting a square internally on the side BC. This leads to the A^--inscribed square. The triangle DeltaX^-Y^-Z^- of centers of the A^--, B^--, and C^--inscribed squares form the outer inscribed squares triangle, which is perspective to DeltaABC with the inner Vecten point, Kimberling's X_(485), as its perspector.

The triangle has area

 Delta_I=(a^2b^2c^2cosAcosBcosC)/(2(a^2-2Delta)(b^2-2Delta)(c^2-2Delta))Delta,

where Delta is the area of the reference triangle.


See also

Inner Inscribed Squares Triangle, Triangle Square Inscribing

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Cite this as:

Weisstein, Eric W. "Outer Inscribed Squares Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OuterInscribedSquaresTriangle.html

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