ORMC Meetings • 2020-2021 Academic Year

Many nontrivial Olympiad problems can be solved by angle chasing. This class we covered inscribed angles, cyclic quadrilaterals, and properties of the orthocenter.

Directed angles, incenter/excenter lemma, problems.

More advanced angle chasing problems

Power of a Point and Radical Axis

Harder problems with Power of a Point

Today we did three challenging problems whose solutions involved Power of a Point in a fundamental way.

We will introduce Ceva's Theorem, Menelaus' Theorem, the Extended Law of Sines, and some basic length formulas in a triangle.

Two proofs of Heron's Formula; Nine-Point Circle, Euler Line, Monge's Theorem

Simson line configuration (including proof that Simson(P) bisects PH) and incenter touch-point configuration.

We will go over the winter break geometry homework and review last quarter's material, and do some Olympiad problems from other subjects if time allows.

Complex numbers and AIME problems

AIME Number Theory problems, which tend to be computational

reviewing the 2021 USAJMO

A few tricks for sums on olympiads

Also discussion of finite abelian groups

Dirichlet's theorem on arithmetic progressions, an comprehensive outline thereof

This involves many standard manipulations of sums, complex numbers, and bounding arguments