To prove it use a

To handle the general case consider the affinity F mapping the equilateral to the general triangle. Since F preserves ratios and parallelity, it maps the whole configuration to the corresponding of the general case, thus transfering the relations verbatim.

By the way, notice that this special parabola (its reflexion on the horizontal axis DE) is represented in orthogonal axes in which |AG|=2 by the function

Parabola.html

ParabolaChords.html

ParabolaSkew.html

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