GSPkc F(!&capmdt%_7ToT0TTv0tTF  Drag Point C.tXjToT0TTv0tTF  Drag Point C.t:ToT0TTv0tTF  Drag Point C.tg6l;? U Hde Segment Trisection @@DC tglC| ToFpoLx:E8D>@DC t SoF o< 0CC t6; Rce, when angle ABC is 60 degree, point D' is 2/3 [=60/90] of the way CC t_d7T QCCD>C WCpBoDpBSP CCP DBC.C t_d Po \ 7T2Ho o ` CSC t{ o O7Tp7.4 o,7T7TBSC t{7T N0h7T. o o o0h`(7TB.C t   B) . 3 F M R X a e CC taf   A         DC t|QNqA IConstruct a square on AB and inscribe an arc that cuts through the angle.?t}sCreate point D' according to this definition: the ratio BD'/BD is the same as the ratio Arc(AC)/Arc(AD). For instance, when angle ABC is 60 degrees, point D' is 2/3 [=60/90] of the way to point D.t|pqrsuvwxz{|}~Construct a perpendicular to BD through D, and the point T where this line intersects BC. The locus of point T is the trisectrix.t{ r7"    }Construct a perpendicular from T to AB. Trisect this segment. Construct lines through the trisection points parallel to AB.t{<ljaThe points where these lines intersect the trisectrix are the points on your new trisected angle!tzo)U{zxwv u s!r!q"p"n#m#k$j$h%g%d&cTa-da!t|@RStart with an angle ABCt 6 : ,, ,0X1The Trisectrix of Hippiast 8 0 z60 |0&3Created by Michael Buescher, 2002 mbuescher@hb.edut #  me|h}C0.m{!:A}ABC -- drag me Drag point C t8j p2?@DC@DCCCCC t5l; al@DCCC? tf5l ak T(@DC@DC? tl aj oo ShowCC@DC? t57 aiisection &@  X' B@?'CCCC? t}b  p1?CSCBSCB.CC.C  tzd ahC.CB.C?  t^dC agDN)CXChWCDhWCFDN)C FCN)CH3DN)C CSCC.C? tzd7T afX 7T77T07TBSCCSC? tz# ae7Tt 7r F{RF|F|B.CBSC? t38?Drzʣ:@T :@N@ X' T?'CTB t5dc1BBBBBBBBB{{{{{{{{BB{{{{{CCQCF%5?F%5? tf  j /58>COUDCCC? t  xCCDC? t3 m16 X: BD = Distance(B to D) = " tE m14}t MS Sas Serif m10 m{!:A}ABD = Angle(ABD) = "t5dQC "a1SVW]S^Pyu3=>C];)t#EPu uv t#CCQC5?5DCCTB# "t&:O0 I m3x04800000 HGW=0x8000 HGW2EXE0x8000 HGW3EXE=0x8000 HJDRAW=0x00400DB = Distance(D to B) = " t2 # lMZ@CTBCC? "tOT*  CjW:@ &@ @ X' ?'i9C$B#tE m13 m{!:A}ABC = Angle(ABC) = +t280800mR2{D:m{!:A}ABC}{90}= THLP0x0004 QAPLUSW=0x0004 QLIIFAX=0x0040@CTBCTB?*"t H5n  m1: [fonts] [FontSubstituts] Helv=MS Sans Serif Tms Rmn=MS Ser m{!:A}ABC = Angle(ABC) = + tN  kCCi9C$B?+ t  uGxCCi9C$B?+ t( m17ppppppppppppp {D:m{!:A}ABC}{m{!:A}ABD} = Angle(ABC)/Angle(ABD) = ,'t,}P m4p {D:m{!:A}ABC}{3} = Angle(ABC)/3 = .t`fAV=0nB=0x04008000 SPORTJEC002P0 SPWIN20=0x00400000 ST2=0x4008022 D@CDC?- t48 m2ppppppppppppp {D:m{!:A}ABC}{90} = Angle(ABC)/90 = ?.ta3f8 M/NDTB 3-tTY%A'         D>C  2t,0 m5ppppppppppppp 2{!:*}{D:m{!:A}ABC}{3} = 2*(Angle(ABC)/3) = 2ty~`P&D'rzʣ:@T :@N@ X' T?'CAB " 4 t`2f  ad 'EX0\\ 7TFDTBDC? 5 t2f8 ac'E 'ECTBDTB?5"t6F m15Iౄ N 5 " y4TyDBD' = Distance(B to D') = 8 tY  rPPVCCD>C?6 t0~5zDLl%A''ʣ &@ @ X' B@?' D AB  7tx~0020oTUP=0x00200000 TL6=0x08000000 TME=0x0100 TMSWIN=0x20000000 TMTWIN=CAB@CAB?38 t vCCD>C?6 tk Hide Square and Arc @ X' B@?'  (9:*"t"Wik Step One.7  < 0  (9:*"tL m18ppppppppppppp {D:BD'}{BD} = %Distance(B to D')/Distance(B to D) = ;& t}5 q2By 2{!:*}{D:m{!:A}ABC}{3}CC D AB?= tayf~h_a~ L\mydocu~1\math_a~1\austra~1\skeches\version3\Anygraph.gspDAB >3ty~ Tʣ:@T :@N@ X' T?'4CAB/>t@ Hide Point D'@'E ¢1%@ X' 袀?'  !81Bt{g Step TwoL n n`bG MNbN !81B txf~ abCABDAB?D8't.( ?Tʣ:@T :@N@ X' T?'E(#+/.48>Et p4C cC4CA?$Et< Hide Point TFD 4Fv1 EHt#r Step Three7  +<| H  EHt E4CC $J tx  yFo, poF4CAB4CC?MEt>T'ʣ &@ 9@ X' B@?'4CWC EMt*?T''ʣ &@ @ X' B@?'4C)C EMt@tLLKKJJIIHHGGFFEEDDCWCpDWC?JOtsC)CqD)C?JPtCC''ʣ &O 9@ X' B?' ,D)C CRt~C'ʣW:@T W:@N@ X' T?'fDWC Q<tlK m12$$##""!!  m{!:A}C''BC = Angle(C''BC) = S +tVLk m11m{!:A}C'BC'' = Angle(C'BC'') = T St@KU m10 m{!:A}ABC' = Angle(ABC') = T t] wCC ,D)C?S taf Kde InstructionsEz ¢1%z@ X' 袀?'D)C R3taf loc J袀?'ArialICCo oinTisplayDWC Q3t) I%z@ X' ?'t | CWC Q*t0? H1&8 HLX/t (M2 HC)C R*tu.  Hide Final_@'E~ ¢1%~@ X' 袀?' C 4 ST?XWVUt"@iT Step FiveD*"*`bG D BST?XWVU tfts a aa< oge the parCWCDWC?Z[ tf, z.E, HotFX oVC)CD)C?Y\t Hide Segment TrisectionFv1 IOPN`_t"j# Step Four7  &<  IOPN`_t Back to the Beginning s<\ h  @FKa]DMS Sans Serif DCArialLxC(Cw