# An Archimedean Lemma

Geometry Level 4

Select two points $$A({x}_{1}, {y}_{1})$$, $$B({x}_{2}, {y}_{2})$$ on the curve $y=px^2+qx+r.$ For which point on the curve $$C({x}_{3}, {y}_{3})$$, between points A and B, is the area of triangle ABC maximum? Express

$\frac{{x}_{3}}{{x}_{1}+{x}_{2}}$ as a decimal.

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