KURSCHAK 1995 Problem 3

Points $A$ , $B$ , $C$ , $D$ are such that no three of them are collinear. Let $E=AB\cap CD$ and $F=BC\cap DA$ . Let $k_1$ , $k_2$ and $k_3$ denote the circles with diameter $\overline{AC}$ , $\overline{BD}$ and $\overline{EF}$ , respectively. Prove that either $k_1,k_2,k_3$ pass through one point, or no two of them intersect.