GSPk F  capm7t B<l  p pp <| 8Method to make four collinear point Harmonic. (1) Given any three colinear points A, X and B, draw point P above the line. (2) Join points X and P. (3) Put a point S anywhere on line XP. (4) Draw lines AP and BP. (5) Draw extended lines from B through S meeting AP at R and from A through S meeting BP at Q. (6) Draw an extended line through R and Q to meet the original line at Y. t.'p @p5,pLxrMg,8DHarmonic Condition:t/oO poP l po lD@pC0Distances are signed positive from left to righttF A0 s  t tlgFXFf؃~} ~tFjhVP>G  CC tsx BhEV:uRFFF:FFPOG jhRP@]DC tzvF  P?(2"H 1ZH 0Z袜GCPC t/$ All points may be draggedt PKH  j\u3ɉ~*^&GF<*t?u~\t~/t~:tNN uωv CC@]DC?t27R  A! @  N"o  :ȣ| #  PRPBC t>  X?(2"H G # *7d$t:HK袜GlCC tCH)H~>  B?(2"  7T$:HK0 VCC  t1>F  k gA/G t gA/ gA/v FVf+fFfNgA3t?~u=3~PBCCPC? tB>  l&_gfwjFVF ~F o0CCCPC? tvQ  m0sA+fNfgA<v42FVfNgAgA2CPClCC? t7[Jm4 YB{!:*} -1 = -4.35 c AX = Distance(A to X) = tKZ^m5 XB = Distance(X to B) = t(]-be?  S @c  N"o  Bȣ| #  PRmCOGC  tb>Hff  nv#fNfgA ~tf3 ^ffNfgqgA.u^GtgF3CCmCOGC? t1-!  o^G`t&ufvjjvʚGQ F4o0PBCmCOGC? t  R @c  N"o  :ȣ| #  PŘCEC t`DeI  Q @c  N"o  6ȣ| #  PRC-C  t,  p0̌CECC-C?tCH  Y?(2"X H G #X L<)7j$t:HKG}0DC ta" m1@DʋCw]C CxC< DL;C CxCFDL;C o ND@ AY = Distance(A to Y) =  t#Z6etchm2D@DArial!o08$D:\SKETCH\NEWF YB = Distance(Y to B) = t`2 pYB= ce(Y to B) p YB{!:*} -1 = YB =  t W1 p m6lppppppppppppp ${(:{D:AY}{YB}}{!:*}{(:{D:XB}{AX}} = <(Distance(A to Y)/YB)*(Distance(X to B)/Distance(A to X)) =  "Arial