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
Here are 16 propositions involving a real number $x$:
[Note: the trig functions are measured in radians]
By choosing $p$ and $q$ from this list, how many correct mathematical statements of the form $p\Rightarrow q$ or $p\Leftrightarrow q$ can you make?
It is possible to rearrange the statements into four statements $p\Rightarrow q$ and four statements $p\Leftrightarrow q$. Can you work out how to do this?