THE IN-AND-CIECUMSCEIBED TEIANG-LE.. 
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Case 14. c=e=x, « = B =y. 
z =(Y-2>D(a ? -l)F 'y, tf=YsD(x-l)Y(y-2), 
g=2x(x-l)(Yy-Y-y)D'F. 
Case 15. F=B=a?, D=e=y. By reciprocation of 14. 
No. =2X(X-l)(Yj/-Y -y)ac. 
Case 16. c=e=x, I)=F=y. 
x =BxY(x-l)(Y-l)a, y!=Yx(Y-l)(x-l)B a(= x ), 
g=2^-l)Y(Y-l)«B. 
Case 17. c=e=x, l\=F=y. 
y=V(x- l)Ya(Y-l)x, y!=Ya(Y-lJxD(x - 1 )(=-/?, 
g = 2x(x — 1 ) Y( Y — 1 )«D . 
But we have here aJ) as an axis of symmetry, so that each triangle is counted twice, 
or the number of distinct triangles is =4g- 
Case 18. a=D=x, c=B=y. 
y=Y(y-2)XeFx, y!=TeXy(Y-2)x(=y) 7 
g =2xX(Yy—Y—y)eF. 
Case 19. c=F=x, e=B=y. 
X =Y xVyXa, y!=XyT)xYa(= x ), 
g = 2xyXYaD. 
Case 20. c=J)=x, e=Y=y. 
X =Bx(X-2)y(Y-2)a, y!=Y(y-2)X(x-2)Ba, 
g = {xy(X-2)(Y-2)+XY(x-2)(y-2)}o-B 
=2{xyXY-xy(X+Y)-XY(x+y)+2xy+2XY}aB„ 
Case 21. c=B=.r, e=F=y. 
x =X(x—2)Dy(Y —2)ci, y! =Y(y-2)Dx(X-2)a, 
S = {X(Y-2)y(x-2)+Y(X-2)x(y-2)}aB 
= 2 {xyXY - xy(X+Y) - XY(x +y)+ 2xY + 2 yX } al). 
Case 22. a=D=x, c=F=y, e=B =z. 
7 =ZyXzYx, ■ x !=YzX !/ Z.r(= x ), 
g=2xyzXYZ. 
