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 1 of 5: Choose the inversion
Detailed analysis
Let T be the tangency point of the given externally tangent circles. Use the inversion centered at P with radius PT. The common tangent PT is fixed by this inversion.