frame(-14,-7,5,6.5)
O = point(0,0)
I=point(1,1)
xax=line(O,I)
T1 = point(xax,-3)
T2 = point(xax,1)
T3=point(xax,7)
P=point(-3,6)
draw(P)
lp1=line(P,T1)
lp2=line(P,T2)
lp3=line(P,T3)
draw(lp3,dotted)
draw(lp2,dotted)
draw(lp1,dotted)
A=point(lp1,1.8)
B=point(lp2,2.0)
C=point(lp3,1.3)
X=point(lp1,4.0)
Y=point(lp2,5.0)
Z=point(lp3,4.3)
draw("$A$",A,160:)
draw("$B$",B,-70:)
draw("$C$",C,20:)
draw("$X$",X,-150:)
draw("$Y$",Y,-140:)
draw("$Z$",Z,140:)

bc=line(B,C)
ca=line(C,A)
ab=line(A,B)
xy=line(X,Y)
yz=line(Y,Z)
zx=line(Z,X)
color(blue)
draw(bc)
draw(yz)
color(red)
draw(ca)
draw(zx)
color(green)
draw(ab)
draw(xy)
thickness(2)
color(black)
draw(X,Y,Z)
draw(A,B,C)
draw(intersection(bc,yz))
draw(intersection(ca,zx))
draw(intersection(ab,xy))
draw(line(intersection(bc,yz),intersection(ab,xy)),dashed)