Find the sides of a tetragon Let ABCD is a tetragon with its cyclic (outer circle). Diagonal BD bisects angle ABC. The intersection point of BD and AC diagonals is point E. BC = 20, CD = 15, CE=12. Please help me find AD, ED, angle BCD and the area of tetragon ABCD. I have tried to find the relationship between the half angles of B, with side AD, but in fact I could not find any.

_Start of an answer:_ Note that since equal angles subtend equal arcs of the circle, the (shorter) arc CD equals the (shorter) arc DA, since they are subtended respectively by angles CBD and ABD, each half of angle ABC. And the chords formed by equal circular arcs are equal, so that chord CD must equal chord AD in length. Since CD=15 that means that also AD=15.