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In Delta ABC,AB= AC, BE and CF are resep...

In `Delta ABC,AB= AC, BE and CF` are resepectively the bisectors of `angle ABC and angle ACB` and itersect the sides AC and AB at the points E and F resepectively. Then four points B,C,E,F are not concylic.

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False since in `Delta ABC, AB= AC`.
`angle ABC= angleACB or, (1)/(2) angle ABC=(1)/(2) angle ACB or, angle EBC= [ :. BE and CF` are the bisecotrs of `angle ABC and angle ACB` respectively.]
Now in `Delta ABC and Delta BFC` we get,
`angle EBC = angle BCF= angle FBC and BC` is common to both.
`:.Delta BEC~= Delta BFC` [ by the A-A-S condition of congruency]
`:. angle BEC= angle BFC`. But they are two scuh angles on the same side of BC at the points Eand F that they are equal .
`:. B,C,E,F` are concyclic.
But given that B,C,E,F are not concyclic.
Hence the given statement is false
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