1. The circle has the center (0, 0) and the radius 4.

The circle has the center (6, 0) and the radius 2.

2. Use similar right triangles to determine the missing lengthes. I used Euklid's theorem to calculate the coordinates of the tangent points:

and

3. The center of the resulting circle must be on the x-axis and on the perpendicular bisector of

The slope of this perpendicular bisector equals the slope of

The midpoint of has the coordinates . That means

4. The perpendicular bisector through M has the equation:

This line crosses the x-axis at:

5. The center of the resulting circle is C(3, 0). Now calculate the distance to get the radius of . I've got . Therefore the equation of is: