What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
Four identical right angled triangles are drawn on the sides of
a square. Two face out, two face in. Why do the four vertices
marked with dots lie on one line?