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Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

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Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.


Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

The diagram is



Without loss of generality you can takethe radii of the two identical circles to be 1 unit.


Using Pythagoras theorem can you then find the radius of the small circle? Don't worry if you get surds in the answer.