Nice Euler Line Problem

Geometry Level 3

Consider \(\triangle ABC\), with \(A=(0,0), B=(5,-10), C=(-24, 7)\).

The slope of the Euler line for \(\triangle ABC\), in its simplest form, can be written as \(\frac{a}{b}\).

Point \(D\) is the centroid of \(\triangle ABC\), whose coordinates can be written as \((d,c)\).

If \(ac+bc=x,\) what is \(x+6713.8\)?


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