DE-MO 2019 Problem 2

Let $a$ and $b$ be two circles, intersecting in two distinct points $Y$ and $Z$ . A circle $k$ touches the circles $a$ and $b$ externally in the points $A$ and $B$ .

Show that the angular bisectors of the angles $\angle ZAY$ and $\angle YBZ$ intersect on the line $YZ$ .