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D\ a n d\ E are points on equal sides ...

`D\ a n d\ E` are points on equal sides `A B\ a n d\ A C` of an isosceles triangle `A B C` such that `A D=A Edot` Prove that `B ,\ C ,\ D ,\ E` are concyclic.

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In `/_\ABC`,
we have
`AB AC`
`/_B = /_C`........`(i)`
In `/_\ADE`,
`AD = AE`
`/_D = /_E`..........`(ii)`
We can write
`/_A + /_D + /_E = /_A + /_B +/_C`
`2/_D = 2/_C`
or
`/_D = /_C`.......`(iii)`
Now
`/_ADE + /_BDE =180^@`But
`/_ADE = /_BCE`
[Using `(i) and (ii)``(iii)`[Linear pair]{By `(iii)`]
`/_BCE + /_BDE = 180^@`
`⇒ B, C, E and D` are concyclic.
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RD SHARMA-CIRCLE -All Questions
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  2. A B C is an isosceles triangle in which A B=A Cdot If D\ a n d\ E ar...

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  3. D\ a n d\ E are points on equal sides A B\ a n d\ A C of an isosce...

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