If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0
what can you say about the triangle?
Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
Prove that if a is a natural number and the square root of a is
rational, then it is a square number (an integer n^2 for some
A graph is a network of points and lines. The points are called
vertices and the lines which connect them are called edges. Each
edge has a vertex at each end. The branch of mathematics called
graph theory studies the properties of various kinds of graphs.
A connected graph is a graph in which we can get from any vertex
to any other by travelling along the edges. A tree is a connected
graph with no closed circuits (or loops).
Prove that every tree has exactly one more vertex than it has