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Lunar Angles

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

Spirostars

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

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?

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).