
The most basic objects of study in elementary synthetic geometry are points, lines, and circles. The circle being the most `complex' of the three, has a much higher number of results associated with it. Despite this complexity, it has a high degree of symmetry which often simplifies the proofs.
1. Basic properties of secants and tangents
2. Cyclic quadrilaterals
3. Power of a point
4. Radical axis
5. The radical axis concurrence theorem