`Da n dE` are points on equal sides `A Ba n dA C` of an isosceles triangle `A B C` such that `A D=A E` . Prove that `B ,C ,D ,E` are concylic.

Explanation

Given – In `triangleABC, AB = AC` and `D` and `E` are points on` AB` and `AC`
Such that `AD = AE. DE` is joined.
To prove `B, C, E, D` are concyclic.
Proof –
In `triangleABC, AB = AC`
`angleB=angleC ` [Angle opposite to equal sides]
Similarly, In `triangleADE,AD=AE` [Given]
`angleADE=angleAED` [angle opposite to equal sides]
In `triangleABC`
`(AP)/(AB)=(AE)/(AC)`
`DE II BC`
`angleADE=angleB` [corresponding angle]
`angleB=angleC`[proved]
`angleADE`=its interior opposite `angleC`
`BCED` is a cyclic quadeilateral
Hence `B,C,E` and `D` are concyclic.