Preliminaries

Four centers

• Orthocenter H - altitudes - Orthic Triangle
• Centroid G - Medians - Medial Triangle
• Incenter I - Incircle - Inradius
• Circumcenter O - Circumcircle - Circumradius

Notations and Conventions

• semiperimeter of $\triangle{ABC}$: $s=\dfrac{1}{2}(a+b+c)$
• $[P_1P_2…P_n]$: area of polygon $P_1P_2…P_n$, $[ABC]$: area of $\triangle{ABC}$
• $(P_1P_2…P_n)$: the circle of cyclic points $P_1, P_2,…,P_n$
• $\measuredangle$: directed angle
• $\overline{AB}$: segmant $AB$ or line $AB$
• $\overline{AB} \cap \overline{CD}$: intersection of two lines $AB$ and $CD$
• $\displaystyle \sum_{cyc}{f(a.b.c)} = f(a,b,c)+f(b,c,a)+f(c,a,b)$

Part 1 Fundamentals

Chapter 1 - Angle Chasing

Inscribed Angle Theorem