This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different?. . . .

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

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.

How far should the roof overhang to shade windows from the mid-day sun?

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?