Two Circles With Inner Contact, Line Outside The Circle

Steps

1. Given two circles tangent at point T and a line that lies outside them.
2. Draw a line h that passes through the centres of the two circles
3. Create an arbitrary point P through which we draw a perpendicular line i to the given line. Find point G - the intersection of lines i & h.
4. Draw a circle e centered at G with radius |GP|. Label the intersections of the circle and the lines i & h with different letters (H, I, J).
5. Draw a line k passing through the points H & P.
6. Draw a line j parallel to the line k passing through the tangent point T.
7. Find the intersection K of line j and the given line. Draw the perpendicular line l that passes through K. The intersection of lines h & l is the center of the first solution.
8. To find the second solution draw a line m that passes through points I & P.
9. Draw a line p that is parallel to line m and also passes through the tangent point T.
10. Find point L - the intersection of lines h & p. Then draw a line q through this point perpendicular to the given line. The intersection of lines h & q is the center of the second solution.