# Triangle defined by one point

Geometry Level 5

Point $$H(1,2,3)$$ is an orthocentre of a triangle. Vertices of a triangle are on the axes of the coordinate system. $$O$$ is circumcentre of the triangle, $$R$$ is radius of triangle's nine point circle and $$N$$ is centre of the nine point circle.

Find $$R^2 - ON^2$$

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