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Consider three circles $(O_1)$, $(O_2)$, $(O_3)$. Denote the homothetic center of $\{$$(O_1)$, $(O_2)$$\}$ by $A$, the homothetic center of $\{$$(O_2)$, $(O_3)$$\}$ by $B$. Let $C$, $D$ be two points on the line $AB$. Then the tangent lines from $C$ to $(O_3)$ and the tangent lines from $D$ to $(O_1)$ form a tangential quadrilateral, i.e. they are all tangent to some circle $(O_4)$, as in the figure.

Does this theorem have a name?

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