CMO 1974 Problem 5

Given a circle with diameter $AB$ and a point $X$ on the circle different from $A$ and $B$ , let $t_{a}$ , $t_{b}$ and $t_{x}$ be the tangents to the circle at $A$ , $B$ and $X$ respectively. Let $Z$ be the point where line $AX$ meets $t_{b}$ and $Y$ the point where line $BX$ meets $t_{a}$ . Show that the three lines $YZ$ , $t_{x}$ and $AB$ are either concurrent (i.e., all pass through the same point) or parallel.