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?
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?
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.
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.