Collinear intersection of tangents

This interesting problem was to show that if there are 3 circles and each have a pair of common tangents to other the intersection of the 3 intersecting pt lies on a line. The challenge was to draw 3 circles and then draw tangents. It becomes interesting when one starts with two circles. Since its pretty easy to start with a line and then make two circles on it which will always remain tangent, no matter how you change the shape. The second tangent can be drawn pretty easily by reflecting. However incorporating the third circle such that one can draw parallel tangents was giving me problem. I had a good discussion with Dr. Kocik regarding this. Yesterday around 3:am as I was about to goto bed (inspite of promising myself to go to bed early) I had an idea why not draw a triangle first and then draw circles inside it in this way I start with each of the 3 circle having a pair of tangents and all I would then need is to draw the 2nd tangent which my intuition said would be easy and after a 20 minute bout with KIG. I had the drawing working perfectly. I repeated it again on GeoGebra and it came out nicely. In the morning I tried on KSEG and this is the output. I have hided the clutter so you can see the nice geometry.