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 $\mathrm{△}ABC$: $s={\displaystyle \frac{1}{2}}(a+b+c)$
• $[P_1{P}_2\dots P_n]$: area of polygon $P_1{P}_2\dots P_n$, $[ABC]$: area of $\mathrm{△}ABC$
• $(P_1{P}_2\dots P_n)$: the circle of cyclic points $P_1,P_2,\dots ,P_n$
• $\measuredangle$: 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