Here's another quiz. Please refer to the drawing below:
On a piece of paper, draw 3 non-overlapping circles of different sizes, and let's name the circles a, b, and c. Draw the tangents from circle a to circle b and extend them until they meet at point AB. Do the same for all three circles such that there are 3 intersection points AB, AC and BC.
From the example shown here it is apparent that points AB, AC and BC fall on a straight line. How to prove that the 3 points always fall on a straight line as long as the 3 circles are of different sizes and do not overlap each other?