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:
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: