GR-HMS 2013 Problem 4

Let a triangle $ABC$ inscribed in circle $c(O,R)$ and $D$ an arbitrary point on $BC$ (different from the midpoint).The circumscribed circle of $BOD$ ,which is $(c_1)$ , meets $c(O,R)$ at $K$ and $AB$ at $Z$ .The circumscribed circle of $COD$ $(c_2)$ ,meets $c(O,R)$ at $M$ and $AC$ at $E$ .Finally, the circumscribed circle of $AEZ$ $(c_3)$ ,meets $c(O,R)$ at $N$ .Prove that $\triangle{ABC}=\triangle{KMN}.$