Angle Chasing
Label everything, then keep going.
The default opening move in olympiad geometry: mark every angle you can name, propagate with the circle theorems, and see what collides. The engine is the inscribed angle theorem: an angle at the centre is twice an angle at the circumference on the same arc.
The three tools you will reach for constantly: equal angles on the same arc (which also proves four points concyclic), opposite angles of a cyclic quadrilateral summing to , and the tangent–chord angle equalling the inscribed angle in the alternate segment.
When a problem asks you to prove a concyclicity, it is nearly always asking for two equal angles on a common segment. When it asks for a fixed angle, look for an arc that never moves.
Train it on Lemma
Angle Chasing unlocks at Level 3 of Lemma's eight-level ladder, with lessons that teach it and drills that make it stick. 125 lessons, 1206 curated problems and unlimited generated practice at six difficulties. Free to start, no card, and every paid plan opens with 3 free days.
Find your levelMore techniques
- Working BackwardsStart at the end. The end knows more.
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