Find ∠BDE in a Circle: BDC is a Minor Arc with ∠BOC = 110°

[nothing123]

1. BDC is a minor arc of a circle, centre O. CD is produced to E. If ∠BOC = 110°, find the number of degrees in ∠BDE.

this is the diagram i came up with,

http://img209.imageshack.us/img209/2500/circle4hm.jpg

by experimentation (i know it's weak), i found ∠BDE to be 55, exactly half of ∠BOC and i can't find a theorem to relate to this. anyone have ideas?

thanks.

 

[Fermat]

If you draw a point P on the major arc of OBC, then there is a theroem which states that: ∠BOC = 2*∠BPC.
You still need another theroem though, about the opposite angles of a cyclic quadrilateral. Can you find that?