ABC is an isosceles triangle in which AB=AC IF D and E are midpoints of AB and AC respectively, prove that B,C,D and E are concyclic.

Please reply soon.

Given: ABC is an isosceles triangle with AB = AC

D and E are the mid points of AB and AC

Now in ∆ABC

∠ABC = ∠ACB  (angles opposite to equal sides are equal)

⇒ ∠DBC = ∠ECB          ...  (1)

and since D and E are mid point of AB and AC

∴ DE || BC           (mid point theorem)

⇒ ∠EDB + ∠DBC = 180°          (Linear pair)  ...  (2)  

from (1) and (2)

∠EDB + ∠ECB = 180°

Since opposite angles of quadrilateral DBCE are supplementary

Hence points B, C, D, E are concyclic