Does this helps? http://whistleralley.com/tangents/tangents.htm See the gergonne solution somewhere at the bottom of the page.

Can someone post a solution? The link does not open for me.

Gergonne's Solution: Draw the six pairwise internal and external homothetic centers of the circles. These there are $4$ lines that go through $3$ each of these points by Monge's Theorem. Take one of these lines, and construct the poles of this line with respect to each of these circles. Then take the radical center of the three circles, and connect it to each of the poles. Intersect each connector with its corresponding circle twice. These make two sets of three points, which define a pair of complementary circles that are tangent to each of the three other circles. If we use the other three lines, we can construct six other circles, for a total of $8$ circles.