Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

There are many different methods to solve this geometrical problem - how many can you find?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?