Two circles that are not congruent:

Two circles, [math]\gamma[/math] and [math]\gamma'[/math], with centers [math]C[/math] and [math]C'[/math] respectively, are externally tangent at point [math]T[/math].[br]A line through [math]T[/math] intersects [math]\gamma[/math] at [math]A[/math] and [math]\gamma'[/math] at [math]B[/math].[br]Show that [math]AC\parallel BC'[/math].

Two circles with centers at [math]C[/math] and [math]C'[/math] are congruent and secant at points [math]A[/math] and [math]B[/math], and each passes through the center of the other. [br]Show that the line [math]AB[/math] is the angle bisector of [math]C\widehat{A}C'[/math].

Two circles with centers at [math]C[/math] and [math]C'[/math] intersect at points [math]A[/math] and [math]B[/math]. [br]Show that the line through the centers is the perpendicular bisector of segment [math]AB[/math], and that [math]C\widehat{A}C' \cong C\widehat{B}C'[/math] .