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AMO 2027 Grades 9-11 SET 3 - Self-study Question 13

AMO · AMO 2027 Grades 9-11 SET 3 - Self-study

Question 13

A circle of radius 1 rolls without slipping around the inside of a right-angled triangle with side lengths 9, 12 and 15, returning to its starting point after one circuit. How far does its centre travel? Use the source's idealized path: along each side the circle remains internally tangent to that side, transferring at a position tangent to two sides; no extra looping motion is included.

Question illustration

Enter one positive integer, without units.