A circle passing through the origin has the general equation x^2+y^2+Dx+Ey=0 (no constant term); its intercepts on the x-axis and y-axis are 0 and -D, and 0 and -E respectively, and its centre is located at (-D/2, -E/2).
For a circle through the origin, x^2+y^2+Dx+Ey=0. Setting y=0 gives x-intercepts at x=0 and x=-D, so the chord length on the x-axis is |D| =...
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