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Question
ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that AD || BC .
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Solution
If ABCD is a cyclic quadrilateral in which AB and CD when produced meet in E such that EA = ED, then we have to prove the following, AD || BC
It is given that EA = ED, so
Since, ABCD is cyclic quadrilateral
`x + angleABC = 180 ⇒ angleDAB = 180 - x`
And ; ` x + angleBCD = 180 ⇒ angle BCD = 180- x `
Now,
`angle DAB + angle ABC = x + 180 - x = 180`
Therefore, the adjacent angles `angleDAB ` and `angleABC` are supplementary
Hence, AD || BC
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