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.
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