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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?


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.

Just Touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?


Age 16 to 18
Challenge Level

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.