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 perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

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.

Circles in Circles

Age 16 to 18 Challenge Level:

Draw lines through the centres of the circles. Write down and
solve some simple equations involving the radii. Remember to use
the exact values involving square roots (irrational numbers).