Angles - points, lines and parallel lines

This diagram has symmetry of order four. Can you use different geometric properties to find a particular length?

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

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?

Weekly Problem 16 - 2007
Can you figure out how far the robot has travelled by the time it is first facing due East?

Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?