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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

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Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Weekly Problem 1 - 2006

Stage: 3 Challenge Level: Challenge Level:1

4 cm

Each centre is 2.5cm from the nearer end. So the distance between them is (9 - (2 x 2.5))cm.

This problem is taken from the UKMT Mathematical Challenges.


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