9 Point Circle of a Triangle Inscribed in a Right Hyperbola

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If a rectangular hyperbola circumscribes a triangle, the center of the hyperbola lies on the 9 point circle of the triangle.

The 9 point circle is the circumcircle of the medians of the triangle’s sides. We see from its equation that it passes through the origin, which is the center of the hyperbola Y=a/X.

Expressions

Name Input
Circle Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image