Let A1,B1 and C1 be points on sides BC, CA and AB of an acute triangle ABC respectively, such that AA1, BB1 and CC1 are the internal angle bisectors of triangle ABC. Let I be the incentre of triangle ABC, and H be the orthocentre of triangle A1B1C1. Show that AH+BH+CH≥AI+BI+CI.
geometryincenterIMO Shortlistorthocenter