0 ,m= `'ca\pm ,x((So2 -Fp#  U[[\\j0jp-(j`0jPijClick and drag point P.j00j-( jj-($ Fp#  PVƣzh  CDC EJ! Fp#  CCC9K>P pi Fp#  Bons of the altitudes and circumircle of a triangle dmw f99urrX<umBC V Fp#  A99uVwhudfOuVE_^[]VWhudfFj,uaCC? \p Fp#  rgAD )x<**tCCCDC?A Fp#  qBCCDC?A Fp#  p9sCC?CDC?J!  Fp#  oCCCC??8JJ!  Fp#  nBCCC?J>  Fp#  m9sCC?BC?> Fp#  lCCCC?? Fp#  kBCCC? Fp#  j9sCC?BC?MH  Fp#  p2""??n n n n , ?CCCC?BCAF Fp#  D h%v~Rh@Lh%v~RF@CX|C  ’ Fp#  E h%v~Rh@Lh%v~RF@CjCDK in* Fp#  Ffƣvh  BjC{ 6 Fp#  m1066pp777! Area BAC = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Area(Polygon BAC) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>?D Fp#  HC5C hm Fp#  IBC}   Fp#  ahCjCDKCC??J!  Fp#  agCCCjCDK?@J!  Fp#  afCX|CCC?8JF  Fp#  aeBCCX|C?J>n  Fp#  adP>'v@) BjC{BC?h  Fp#  acx[„>J?! C) CC?BjC{?F  Fp#  aaCC?CX|C?hJ!  Fp#  z9sCCBjC{?J>  Fp#  yBCCjCDK?hx<=  Fp#   aizYfb_^3zUVWu3W;tu EPECjCDKBjC{?hF^_  Fp#   aj)u3H; )u(H; )u@ )uL$ D$@3 D$ @BjC{CX|C?F;  Fp#   akjDj@tL$ L$ @3^D$; u!PCX|CCjCDK?kD  Fp#  p1P*.gs* altitudes and circumircle of a triangle dmw fGS**.gs*?CX|CCjCDKBjC{gJ!  Fp#   al?D ICCBC}?D  Fp#   amCC?C5C?]  Fp#   m7$$$88IIIIYYiiiiYY))))9999 YY ! m {S:FB} = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Length(Segment FB) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>^ Fp#   m600000000 ! m {S:DC} = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Length(Segment DC) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>] Fp#   m5gle of triangle ABC and pedalpoint P dmw f99 ! m {S:EA} = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Length(Segment EA) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>ZZ Fp#   m366((ll ;;ee7 ! m {S:AF} = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Length(Segment AF) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>1 Fp#   m2QQ>>!!!!!!!! ! m {S:BD} = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Length(Segment BD) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(> Fp#   m1ns of the altitudes and circumircle of a triangle dmw f99 ! m {S:CE} = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Length(Segment CE) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>6I8 Fp#  m11;;22JJ~~DDDD,! Area FED = 6 xh@@ q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((Area(Polygon FED) = "))Lpdžr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>" Fp#  Gfƣvh  C&UUCV #$7 Fp#   m8 ))00EEH !1{(:m {S:FB}}{!:*}{(:m {S:DC}}{!:*}{(:m {S:EA}} = q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((;Length(Segment FB)*Length(Segment DC)*Length(Segment EA) = džr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>%&'7@ Fp#   m4 ))00EEH !1{(:m {S:AF}}{!:*}{(:m {S:BD}}{!:*}{(:m {S:CE}} = q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((;Length(Segment AF)*Length(Segment BD)*Length(Segment CE) = džr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>()* 6*7 Fp#  m12 ))00EEH !!{D:{(:Area BAC}}{{(:Area FED}} = }{(:m {S:CE}} = q#P!h&,+(J,)ģ,0,h&!N+(VjljiL$((p((&Area(Polygon BAC)/Area(Polygon FED) = Length(Segment CE) = džr)%")'Lŀ)L*tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>+tK6 Fp#   m9 ))00EEH !m{D:{(:{(:m {S:AF}}{!:*}{(:m {S:BD}}{!:*}{(:m {S:CE}}}}{{(:{(:m {S:FB}}{!:*}{(:m {S:DC}}{!:*}{(:m {S:EA}}}} = ,0,h&!N+(VjljiL$((p((x(Length(Segment AF)*Length(Segment BD)*Length(Segment CE))/(Length(Segment FB)*Length(Segment DC)*Length(Segment EA)) = tdžr*'(D "alh@H 0*tA: *'D*'8@ h@rX !jHt*FpxP~h&Ϡ,h@ƅnR0!? ?,,@",Y`:fs8Ȝ~: h&:Ǜft(>F6(>.-