MathDB

4

Part of 2003 Kazakhstan National Olympiad

Problems(1)

concurrent lines starting with touchpoint of incircle with triangle

Source: Kazakhstan NMO 2003 grade XI P4

5/12/2019
Let the inscribed circle ω \omega of triangle ABC ABC touch the side BC BC at the point A′ A '. Let AA′ AA ' intersect ω \omega at P≠A P \neq A . Let CP CP and BP BP intersect ω \omega , respectively, at points N N and M M other than P P . Prove that AA′,BN AA ', BN and CM CM intersect at one point.
geometryincircleconcurrencyconcurrent