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Coins on a Plate

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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Semicircle in a Semicircle

Weekly Problem 2 - 2008
The diagram shows two semicircular arcs... What is the diameter of the shaded region?

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