▁the ▁hyp oten use ▁will ▁be ▁a ▁diameter ▁of ▁the ▁circle . ▁A ▁cor ollary ▁is ▁that ▁the ▁length ▁of ▁the ▁hyp oten use ▁is ▁twice ▁the ▁distance ▁from ▁the ▁right ▁angle ▁vertex ▁to ▁the ▁mid point ▁of ▁the ▁hyp oten use . ▁Also , ▁the ▁center ▁of ▁the ▁circle ▁that ▁circ ums cri bes ▁a ▁right ▁triangle ▁is ▁the ▁mid point ▁of ▁the ▁hyp oten use ▁and ▁its ▁radius ▁is ▁one ▁half ▁the ▁length ▁of ▁the ▁hyp oten use . ▁ ▁Med ians ▁The ▁following ▁formulas ▁hold ▁for ▁the ▁med ians ▁of ▁a ▁right ▁triangle : ▁ ▁The ▁median ▁on ▁the ▁hyp oten use ▁of ▁a ▁right ▁triangle ▁div ides ▁the ▁triangle ▁into ▁two ▁is os cel es ▁tri angles , ▁because ▁the ▁median ▁equals ▁one - half ▁the ▁hyp oten use . ▁ ▁The ▁med ians ▁ma ▁and ▁m b ▁from ▁the ▁legs ▁satisfy ▁ ▁E uler ▁line ▁In ▁a ▁right ▁triangle , ▁the ▁E uler ▁line ▁contains ▁the ▁median ▁on ▁the ▁hyp oten use — that ▁is , ▁it ▁goes ▁through ▁both ▁the ▁right - ang led ▁vertex ▁and ▁the ▁mid point ▁of ▁the ▁side ▁opposite ▁that ▁vertex . ▁This ▁is ▁because ▁the ▁right ▁triangle ' s ▁orth oc enter , ▁the ▁intersection ▁of ▁its ▁alt itudes , ▁falls ▁on ▁the ▁right - ang led ▁vertex ▁while ▁its ▁circum center , ▁the ▁intersection ▁of ▁its ▁per pend icular ▁bis ectors ▁of ▁sides , ▁falls ▁on ▁the ▁mid point ▁of ▁the ▁hyp oten use . ▁ ▁I ne qual ities ▁