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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.

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Bishop's Paradise

Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?

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Contact Circles

Weekly Problem 25 - 2010
These four touching circles have another circle hiding amongst them...

Not So Little X

Stage: 3 Challenge Level: Challenge Level:1

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
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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