('A Mathematician's Lament')
Paul's article is worth a read, or a re-read, arguing that maths is fundamentally about problems and these must be made the focus of a student's mathematical life, however painful and frustrating this may be
he describes a student's argument that if you take a right-angled triangle (hypotenuse passing through the centre) and rotate it around (through 180) it creates a four-sided shape, the sides of which must be parallel ...
so it is a parallelogram
further, the diagonals are both the same length ...
so it must be a rectangle
they complete their view that since the triangle got rotated halfway round the circle, one 'tip' ends up exactly opposite from where it started
that's why the other diagonal is also a diameter
and since it's a rectangle the angles are 90 degrees