P23

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

peprendicular from I to AI,BI,CI lead to concurrent

Source: Sharygin Geometry Olympiad 2017 First Round P23 grades 10-11

m

touch the incircle of triangle

ABC

. The lines passing through the incenter

I

and perpendicular to

AI, BI, CI

m

A', B', C'

respectively. Prove that

AA', BB'

CC'

geometryconcurrencyconcurrentperpendicular lines