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In figure, ABE is a in which AE=BE . Cir...

In figure, ABE is a in which `AE=BE` . Circle passing through A and B intersects AE and BE at D and C respectively. Prove that `DC||AB`.

Text Solution

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We are given, `AE = BE`,
`:. /_EAB = /_EBA->(1)`
Also, we know, exterior angle of a cyclic quadrilateral is equal to opposite interior angle.
`:. /_EBA = /_EDC->(2)`
From (1) and (2),
`/_EAB = /_EDC`
As both these angles are equal, it implies `DC` and `AB` are parallel to each other.
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