



 
I wonder if there might be some typographical error in the statement of your problem. Simply assign a fixed value to a and to b. Then P and Q will be fixed points which determine a fixed line. If you replace c by the variable x then R is a an ovalshaped curve, so you can be certain that for most choices of a, b, and c, the points will not be collinear. (Also, since b never appears alone, you can simplify the way the problem looks by replacing ab everywhere with d.) Chris  


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