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 circlesa,b, andc. Draw the tangents from circleato circleband extend them until they meet at pointAB. Do the same for all three circles such that there are 3 intersection pointsAB,ACandBC.

From the example shown here it is apparent that pointsAB,ACandBCfall 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?

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