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ABCD is a parallelogram. The circle through A, B and C intersect CD (produced ifnecessary) at E. Prove that `A E = A D`.

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ABCD is a parallelogram. The circle through A, B and C intersect CD (produced ifnecessary) at E. Prove that `A E = A D`.
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ABCD is a parallelogram
`/_ADC=/_ABC`
Point E also lies on circle ABCE is a cyclic quadrilateral
`/_AEC+/_ABC=180^0`
`/_AEC=180-/_ADC`
`/_AED=/_ADC`
`/AED=/_ADE`
In`/_ADE`
`/_AED=/_ADE`
AD=AE.
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