# Definition of an exercise ruler & compass.
# syntax of the file.
# points:  each line defines a point.  x,y
# lines:   each line defines two points on a line.   x1,y1,x2,y2,type
#          type: 1 (segment), 2 (line), 3 (semiline direct), 4 (semiline inverse)
#	   type is facultative, defaulting to 1.
# circles: each line defines a circle. x,y,r,n
#	   where (x,y) is the center, r=radius,
#          n is the number of point for the center (if n>0).
# goal: each line defines an object. First item is the type of the object
# (point,line or circle), the rest are parameters (same as above).
# goal_text: text explaining the goal. (language-dependent)

title=Trisection d'un segment
boundary=circles
theta=!random 0,2*pi
points=cos($theta),sin($theta)\
-cos($theta),-sin($theta)
lines=-cos($theta),-sin($theta),cos($theta),sin($theta),1

goal=point,cos($theta)/3,sin($theta)/3\
point,-cos($theta)/3,-sin($theta)/3
goal_text=diviser le segment 1-2 en trois
hint=On commence par construire une autre droite, parallle au segment de dpart.\
Ensuite marquer 4 points sur cette droite,  intervalles rguliers.\
Enfin, projeter les 4 points sur le segment de dpart, avec les deux\
extrmits sur les points 1,2.
solution=circle,1,2\
circle,2,1\
point,circle,1,circle,2\
hide,point,4\
circle,3,1\
point,circle,1,circle,3\
line,3,5#Droite 2 est parallle  droite 1.\
point,line,2,circle,2\
hide,circle,1\
hide,circle,2\
hide,circle,3\
circle,5,3\
point,line,2,circle,4#Points 7,5,3,6 sont  intervalles rguliers, donc 3 et 5 divisent 6-7 par 3.\
hide,circle,4\
line,1,7\
line,2,6\
point,line,3,line,4#Point 8 sera la base de la projection.\
line,8,5\
point,line,1,line,5\
line,8,3\
point,line,1,line,6


