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...Formulas for pre olympiad competition math eashang august this is a compilation of various theorems lemmas and facts that are useful i ve ordered them by topic geometry number theory algebra count ing probability it designed to be reference not study guide the starred ones you must know as they very come up in nearly every others listed good fun learn used occasionally but aren t necessary scoring well thanks all aopsers especially mathwiz who contributed through their time suggestions more depth explanations each these visit aops wiki or search on youtube hope helps page area triangle bh rs absin abc r where b base h height second equation inradius s semiperimeter which half perimeter third angle between two sides nal c with circumradius square kite rhombus alternatively d side length diagonal prior only applies squares latter formula applied any quadrilateral perpendicular diagonals such kites rhombi rectangle trapezoid bases regular hexagon deriving breaking into six equilateral tri...