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TOT 228 1989 Autumn A J2 cyclic hexagon, AB=BC,CD=DE, EF=FA

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March 12, 2021
hexagonCyclicgeometryareas

Problem Statement

The hexagon ABCDEFABCDEF is inscribed in a circle, AB=BC=a,CD=DE=bAB = BC = a, CD = DE = b, and EF=FA=cEF = FA = c. Prove that the area of triangle BDFBDF equals half the area of the hexagon.
(I.P. Nagel, Yevpatoria).
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