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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