Problem 14P

The figure shows a parabolic segment, that is, a portion of a parabola cut off by a chord AB. It also shows a point C on the parabola with the property that the tangent line at C is parallel to the chord AB. Archimedes proved that the area of the parabolic segment is 43 times the area of the inscribed triangle ABC. Verify Archimedes result for the parabola y=4×2 and the line y=x+2.

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