Nice Euler Line Problem

Geometry Level 3

Consider ABC\triangle ABC, with A=(0,0),B=(5,10),C=(24,7)A=(0,0), B=(5,-10), C=(-24, 7). The slope of the Euler line for ABC\triangle ABC, in its simplest form, can be written as ab\dfrac{a}{b}. Point DD is the centroid of ABC\triangle ABC, whose coordinates can be written as (d,c)(d,c).

If ac+bc=x,ac+bc=x, what is x+6713.8x+6713.8?

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