To improve AIME score, and to learn methods of solving complicated geometry problems such as Junior MO problems.
Ceva & Menelaus
Transformations
Triangle 5 Centers
Cyclic Quadrilaterals
9 Point Circles & Euler Line
Radical Axis
Circumscribed quadrilaterals
Trigonometry Methods
Solid Geometry
Homothety
Simson Lines and Miquel Points
Harmonic Quadrilaterals
Cross Ratios & Harmonic Bundles
Isogonal Conjugate and Symmedians
Poles and Polars
Vectors and triangle centers
Humpty & Dumpty Points
Spiral Similarity