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. 78 lessons, 624 curated problems and unlimited generated practice at six difficulties. Free to start — no card, no trial clock.
Find your levelMore techniques
- Working BackwardsStart at the end. The end knows more.
- Pigeonhole PrincipleMore pigeons than holes means a shared hole.
- All 26 techniques →