Use the fact that the line CD of middles of AE, BE is tangent to the chord (see ParabolaChords.html ) and area(EDC)=area(ABE)/4. Then use repeatedly a subdivision of the sector as shown to produce a series for the area of the sector and prove it to be 2a/3 (denoting by a=area(ABE)).

MedialParabola.html

Miquel_Point.html

Parabola.html

ParabolaChords.html

ParabolaProperty.html

Thales_General.html

ThalesParabola.html

TrianglesCircumscribingParabolas.html

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