▁one ▁of ▁Peter ▁Y ff ' s ▁not ebook s , ▁written ▁in ▁ 1 9 6 1 . ▁ ▁Definition ▁ ▁The ▁equal ▁par alle li ans ▁point ▁of ▁triangle ▁ABC ▁is ▁ ▁a ▁point ▁P ▁in ▁the ▁plane ▁of ▁triangle ▁ABC ▁such ▁that ▁the ▁three ▁segments ▁through ▁P ▁parallel ▁to ▁the ▁s idel ines ▁of ▁ABC ▁and ▁having ▁end points ▁on ▁these ▁s idel ines ▁have ▁equal ▁lengths . ▁ ▁Tr il ine ar ▁coordinates ▁The ▁tr il ine ar ▁coordinates ▁of ▁the ▁equal ▁par alle li ans ▁point ▁of ▁triangle ▁ABC ▁are ▁( ▁b c ▁( ▁ca ▁+ ▁ab ▁– ▁b c ▁) ▁: ▁ca ▁( ▁ab ▁+ ▁b c ▁– ▁ca ▁) ▁: ▁ab ▁( ▁b c ▁+ ▁ca ▁– ▁ab ▁) ▁) ▁ ▁Const ruction ▁for ▁the ▁equal ▁par alle li ans ▁point ▁ ▁Let ▁A ' B ' C ' ▁ ▁be ▁the ▁ant ic om plement ary ▁triangle ▁of ▁triangle ▁ABC . ▁Let ▁the ▁internal ▁bis ectors ▁of ▁the ▁angles ▁at ▁the ▁vertices ▁A , ▁B , ▁C ▁of ▁triangle ▁ABC ▁meet ▁the ▁opposite ▁s idel ines ▁at ▁A ' ', ▁B ' ', ▁C '' ▁respectively . ▁Then ▁the ▁lines ▁A ' A ' ', ▁B ' B '' ▁and ▁C ' C '' ▁con cur ▁at ▁the ▁equal ▁par alle li ans ▁point ▁of ▁triangle ▁ABC . ▁ ▁See ▁also ▁Cong ru ent ▁is os cel izers ▁point ▁ ▁References ▁ ▁Category : Tri angle ▁cent ers <0x0A> </s> ▁Ba um el ▁is ▁a