Problem 5
Two tangent circles and a point P on their common tangent perpendicular to the line joining their centres are given. Construct with ruler and compass all circles tangent to the two given circles and passing through P.
Step 4 of 5: Construct the two solutions
Detailed analysis
Construct the two common tangents other than PT. For each tangent t, drop the perpendicular from P to t, invert its foot with respect to the circle centered at P of radius PT, and draw the circle with diameter joining P to the inverse point. This is the inverse of t and is tangent to both given circles.