Triangle and Circles

Let $ABC$ be a triangle with $AB < AC$ inscribed in a circle $(O)$, and suppose $\angle CBA = 50^\circ$. A point $D$ lies on side $AB$, different from $A$ and $B$. The circle $(BCD)$ meets side $AC$ again at a point $E \neq C$. Let $P$ be the second intersection point, other than $A$, of the circles $(O)$ and $(ADE)$. The line $PD$ meets $(O)$ again at $K$. Find $\angle ABK$, in degrees.