Illustration of one example where Apollonius' problem has no solutions. The three given circles are red, green and blue. The green circle divides the other two; the blue circle is entirely within, and the red circle is entirely without. Therefore, any circle (such as the black one) that is tangent to both the red and blue circles must cross the green circle; hence, it cannot be tangent to the green circle.
{{Information |Description=Illustration of one example where Apollonius' problem has no solutions. The three given circles are red, green and blue. The green circle divides the other two; the blue circle is entirely within, and the red circle is entirel