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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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Not So Little X

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?

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The Cyclic Quadrilateral

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

Right Angles

Age 11 to 14 Challenge Level:
The problem Triangles in Circles will help if you are having difficulty calculating angles.

Try an even number of points round the edge.

Proving this will be easier if you join all the points to the centre and look for isosceles triangles.