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2006/07 AHSMC Part 1 Problem 6

Problem 6 of 16

On a plane are two points AA and BB at a distance 55 apart. The number of straight lines in this plane which are at a distance 22 from AA and at a distance 33 from BB is

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Solution

Draw a circle with centre AA and radius 22. Draw another circle with centre BB and radius 33. The lines we seek are the common tangents of these two circles, of which there are 33. The answer is (d).

University of Alberta