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

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Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

Not So Little X

Age 11 to 14
Challenge Level

Two circles are enclosed by a rectangle 12 units by x units.

The distance between the centres of the two circles is x/3 units.

How big is x?

Circles in the box