IMO 1969 Problem 4

$C$ is a point on the semicircle diameter $AB$ , between $A$ and $B$ . $D$ is the foot of the perpendicular from $C$ to $AB$ . The circle $K_1$ is the incircle of $ABC$ , the circle $K_2$ touches $CD,DA$ and the semicircle, the circle $K_3$ touches $CD,DB$ and the semicircle. Prove that $K_1,K_2$ and $K_3$ have another common tangent apart from $AB$ .