Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?
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.
Can you create a Latin Square from multiples of a six digit number?
A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?
A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
