▁ ▁Den ote ▁as ▁G , ▁F + , ▁and ▁F − ▁respectively ▁the ▁cent roid ▁and ▁the ▁first ▁and ▁second ▁F erm at ▁points ▁of ▁a ▁triangle . ▁The ▁major ▁axis ▁of ▁the ▁triangle ' s ▁Ste iner ▁in el lipse ▁is ▁the ▁inner ▁bis ector ▁of ▁ <0xE2> <0x88> <0xA0> F + G F − . ▁The ▁lengths ▁of ▁the ▁axes ▁are ▁| G F − | ▁ ± ▁| G F + | : ▁that ▁is , ▁the ▁sum ▁and ▁difference ▁of ▁the ▁distances ▁of ▁the ▁F erm at ▁points ▁from ▁the ▁cent roid . ▁ ▁The ▁axes ▁of ▁the ▁Ste iner ▁in el lipse ▁of ▁a ▁triangle ▁are ▁tang ent ▁to ▁its ▁K ie pert ▁par ab ola , ▁the ▁unique ▁par ab ola ▁that ▁is ▁tang ent ▁to ▁the ▁sides ▁of ▁the ▁triangle ▁and ▁has ▁the ▁E uler ▁line ▁as ▁its ▁direct rix . ▁ ▁The ▁fo ci ▁of ▁the ▁Ste iner ▁in el lipse ▁of ▁a ▁triangle ▁are ▁the ▁inter sections ▁of ▁the ▁in el lipse ' s ▁major ▁axis ▁and ▁the ▁circle ▁with ▁center ▁on ▁the ▁minor ▁axis ▁and ▁going ▁through ▁the ▁F erm at ▁points . ▁ ▁As ▁with ▁any ▁el lipse ▁ins cribed ▁in ▁a ▁triangle ▁ABC , ▁letting ▁the ▁fo ci ▁be ▁P ▁and ▁Q ▁we ▁have ▁ ▁General ization ▁ ▁The ▁Ste iner ▁in el lipse ▁of ▁a ▁triangle ▁can ▁be ▁generalized ▁to ▁n - g ons : ▁some ▁n - g ons ▁have ▁an ▁interior ▁el lipse ▁that ▁is ▁tang ent