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Thanima from Eastlea Community School in the UK looked at the angles at the centre of the circle, as in the diagrams shown below:
When the band is changed form one peg to the next the difference in the angle at the centre will be 40 degrees:
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.
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?
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.