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
Mark a point $P$ inside a closed curve.
Is it always possible to find two points that lie on the curve,
such that $P$ is the mid point of the line joining these two