Construction: Draw segments XZ and YZ

Proof: By theorem of touching circles, points X, Z, Y are collinear.

XZA BZY vertically opposite angles

Let XZA = BZY = a ….. (I)

Now, seg XA seg XZ …….. (Radii of same circle)

XAZ = XZA. = a …….. (isosceles triangle theorem) (II)

similarly, seg YB seg YZ (Radii of same circle)

BZY = ZBY = a …….. (isosceles triangle theorem) (III)

from (I), (II), (III),

XAZ = ZBY

radius XA || radius YB ………. (Alternate angle test)