GSPk@ Fcapmdpt Feuerbach's Theroem states that for any Triangle the Nine Point Circle is internally tangential to the Incircle and externally tangential to the three Excircles. Feuerbach's Point is at the intersection of the Incircle and the Nine Point Circle.tq  Point Circle^R0[|HLA8Feuerbach's Theoremt i kiqi{i{PaIAHH/Touching Triangle Circles: Feuerbach's Theoremt 1tCt1HHiXt1P0CQC t^c0tBt/HHiZt0@0+DC tuRzWA bN |}&!0;D;088eHQOCC  t Ac z@ih <tctd ihtc+DC"DC? ttKW yih <tbtbpihtbCC7CȗC?tRoCQC+DC?tRhYLAnX88CCCQC?t m+DCCC? tcl+DCCQC? ttQckCC+DC? ttW< j2ih Tt4t42`ih t4t42@CQCCC?tAFltm3D@C  tktm1C@C tX]itm2DC  t" I!U@Ev`UEvpSdnUPu@!@ uC)tC tRW4? M ih <tZptZ ihtZzUDrC  tNS]Ѿ L ih <tVtW0ihtW9ߧCC  tMR*? I0ih <tNtO ihtOpCkC  t INܹo Hih <tK`tKihtK]C\.B  t ? E#ih <tCPtC#ihtCpM!Dl C  ta f5Q D_XBDC  tF] acih <tn0tnpihtnPD@CDC? t] ab0ih < tltm ihtmHX388KDCC@C?tRjYpftaatfPtfihC)tC DR2C?  te]Y w ih <t[t[ piht[+DC)DO.C? ttQjY vih <tXtX@ihtX CC4.C C? tRzW t ih <tOtP0ihtPCCѱCPC? t  sih <tLptLihtLCQCxCZ]C? t q"ih <tD`tD"ihtDCQCĥDDC? tRc p&0ih <t@tA &ihtA+DC8-DѣC?t)7.<ptRtpK#O0a@`tp ih`@K#q DC t49otQtoto0ihC C t Pih <tgtgpihtgj"D%oC  t27 N ih <t]t^0 iht^ DY7D tBG Jih <tR`tRihtRZ0C2kC t F @ih <tFtG ihtFD;DERC  !tRO0staetstsPihDCDC?"tRrYqtadtqtrihC C0D C?#tYno@c4ih <thth`ihthuC)tCeBҾiii$tRY@_txt_ t_`ihDYDzCYRD? %tRkYStutStS@ihZ0CCZ0CdB? &tmR' HtrtHtH@ih*DBKDDROC? 't Sih <tt@ttihtt`MC!C )(t  Oih <t`Pt`iht`p8BDC  +t>PCU KPih <tTtU0ihtT6CVC  ,tN*S/ Gih <tI0tIpihtIPDhj0B  -tk Show Incircle  N"o  Nȣ| *  PR "*tf% Hide Incircle  N"o  :ȣ| *  PR *tDa?c5ih <tuPtuihtupMC!CJBF%5?F%5?.t\^mo@ c3ih <ta`taihta4!;0 DY7DZ_CF%5?F%5?%/tS? c2@ih <tUtV ihtU8`Z0C2kC*BF%5?F%5?&0t*cm@ c1ih <tJ@tJihtJ`D;DERCBCF%5?F%5?'1tAF FR'?'?o8jp Oq *t/%CgC4*tAFP FR'?'?o8jp Oq *tO>C߆C 4*t,u@ Show Excircles  N"o  Bȣ| *  PR  567tBpV Hide Excircles  N"o  Zȣ| *  PR  567t`e  Td9D C  7t Hide Feuerbach's Point,0,,3/O 9t Show Feuerbach's Point>dL:ENmR((R`7 d 9t Hide Nine Point Circle8jp Oq *t 4=>t Show Nine Point Circle8jp Oq *th 4=>"ArialA4R