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concurrency wanted, circle concentric with incircle

Source: 2014 Saudi Arabia GMO TST day III p3

July 31, 2020
geometryconcurrencyconcurrentincentermoving points

Problem Statement

Let ABCABC be a triangle, II its incenter, and ω\omega a circle of center II. Points A′,B′,C′A',B', C' are on ω\omega such that rays IA′,IB′,IC′,IA', IB', IC', starting from II intersect perpendicularly sides BC,CA,ABBC, CA, AB, respectively. Prove that lines AA′,BB′,CC′AA', BB', CC' are concurrent.
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