3 out of 3
What does Pythagoras' Theorem tell you about the radius of these circles?
1 out of 3
Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges?
1 out of 3
Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
1 out of 3
Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.
2 out of 3
A point moves around inside a rectangle. What are the least and the greatest values of the sum of the squares of the distances from the vertices?
2 out of 3
Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.
3 out of 3
What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?
3 out of 3
Prove that for every right angled triangle which has sides with integer lengths: (1) the area of the triangle is even and (2) the length of one of the sides is divisible by 5.
Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.
A description of some experiments in which you can make discoveries about triangles.
