Two Externally Tangent Circles, Different Sizes, Point On The Circle

Steps

1. choose point A as the center of a circular inversion, and choose the radius of the circle so that it passes through both given circles, then draw circle k
2. display circles k₁ and k₂ in the circular inversion, circles k₁ and k₂ are created
3. point C is the point of tangency of k_1' and k_2', construct line o from point C perpendicular to line k₂
4. point F is the intersection of circle k₁ and the perpendicular line o
5. construct line k_4' that is parallel to the line k₂ and passes through point F
6. display line k_4' to its inverse image under the circular inversion with respect to circle k, that circle is the solution to the problem