(36.) 
(37.) 
(38.) 
(39.) 
(40.) 
(41.) 
If any line cuts the sides of a triangle in X, Y, Z; the isogonal conjugates 
of A X, B Y, C Z respectively will meet the opposite sides in collinear 
points. 
(Ibid, p. 59.) 
If a line cut the sides in X, Y, Z; the isotomic points of X, Y, Z with re- 
spect to the sides will be collinear. 
(Ibid, p. 59.) , 
If from any point P on the circumcircle of the triangle ABC, P L, PM, 
P N be drawn perpendicular to P A, P B, PC, meeting BC, C A, AB, 
in L, M, N, then these points L, M, N are collinear with ‘circumcentre, 
(Ibid, p. 67.) 
If PL, PM, PN be _|_’s drawn from a point P on the circumcircle to 
the sides B C, C A, AB respectively, and if Pl, Pm, Pn be drawn meet- 
ing the sides in 1, m, n and making the angles L Pl, M Pm, N Pn equal 
when measured in the same sense, then the points 1, m, n are collinear, 
(Ibid, p. 68.) 
If X 'Y Zand X' Y' Z are any two transversals of the triangle AB C: Y 
W’; ZX, X Y* cut the sides B C, C A, AB in collinear points. 
(Ibid, p. 60.) 
If X Y Zand X! Y! Z' be any two transversals of the triangle AB C, and 
and if Y Z', Y! Z meet in P, Z X!, Z' X meet in Q, X Y', X' Y in R, 
then A P, BQ, C R cut the sides B C, C A, AB in collinear points. 
(Ibid, p. 61.) 
the lines AO, BO, CO cut the sides of the triangle ABC in X, Y, Z; 
and if the points X?, Y?, Z1 be the harmonic conjugate points of X, Y, Z 
with respect to B, C; C, A; and A, B, respectively, then X’, Y?, Zire 
I 
—_ 
collinear. 
(Ibid, p. 61.) 
If the inscribed circle touch the sides in X, Y, Z, then the lines Y Z, Z X, 
X Y cut the sides B C, C A, AB in three collinear points. 
(Ibid, p. 62.) 
The feet of perpendiculars from H and G upon A G and A H respectively 
are collinear with K. 
(Ibid, p. 147.) 
If three triangles AB C, A, B, C,, and A, B, C, have a common axis of 
perspective, their centres of perspective when taken two and two, are 
collinear. 
(McClellan—Geometry of the Circle, p. 122.) 
