Decades ago when I was doing my maths O level our teacher gave us a trigonometry poser. Take any triangle. For each angle split the angle into three equal angle drawing straight lines. For each side, two of the nearer lines will meet at a point. So there will be three meeting points. Draw straight lines for the three point to form a small triangle.
The poser is to prove that the small triangle is always an equilateral one regardless of the angles of the original triangle.
There's a wiki article on Morley's trisector theorem which includes a diagram of what I'm talking about. No point in me putting a link here as the wiki address used is one of those which doesn't work on this forum.
The diagram is fairly easy to understand but trying to prove this is one only for mathematicians.
