A , B , E , D are concyclic  

BE bisects DBC

PROVE THAT ......     AE = AD 

IS ABC a straight line?

mine is also same doubt.is ABC is a straight line?

I think ABC is a straight line.

See this.

Let ABC is not a straight line. then let us produce it back untill it intersects c(o,r) at A'.Join A'D and A'E.

Now <DBE=<EBC

So <DAE=<DBE(Angles in the same segment)

Also <DAE=<DA'E

Here <DAE and <DA'E are corresponding angles. And as they are equal so AE || A'E and that is not possible as both intersects at E.

Hence ABC is a straight line.