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AEFD is a cyclic quad. Let angle EBC be x. Then EFC is 180-x, and EFD is x. We also know that BAD is 180- x ( cointerior angles). Hence BAD and EFD are supplementary. Use same technique, let angle BCF be y. Then you will get FDA to be supplementary to FEA. therefore aefd is a cyclic quad.

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Q: Sides bc and ad of a quadrilateral abcd are parallel a circle meets at the side ab at b and e the side CD at c and f prove that the quadrilateral aefd is cyclic?
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