Sec. 6.7 Coordinate treatment of harmonic ranges 101
6.4 If the fixed triangle[Z 1 ,Z 2 ,Z 3 ]is isosceles, with|Z 1 ,Z 2 |=|Z 1 ,Z 3 |,andZis
a variable point on the side[Z 2 ,Z 3 ], show that the sum of the perpendicular
distances fromZto the linesZ 1 Z 2 andZ 1 Z 3 is constant.[Hint. Select a frame of
reference to simplify the calculations.]6.5 Let[A,B,C,D]be a parallelogram,E=mp{C,D},F=mp{A,B},andletAE
andCFmeetBDatGandH, respectively. Prove thatAE‖CFand|D,G|=
|G,H|=|H,B|.