# 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=Barycentre d'un triangle

a=!random 0,2*pi
a1=!random pi/5,2*pi/3
a2=!random 2*$a1,2*pi-$a1

points=10*cos($a),10*sin($a)\
10*cos($a+$a1),10*sin($a+$a1)\
10*cos($a+$a2),10*sin($a+$a2)
lines=10*cos($a),10*sin($a),10*cos($a+$a1),10*sin($a+$a1),1\
10*cos($a+$a1),10*sin($a+$a1),10*cos($a+$a2),10*sin($a+$a2),1\
10*cos($a+$a2),10*sin($a+$a2),10*cos($a),10*sin($a),1

goal=point,10*(cos($a)+cos($a+$a1)+cos($a+$a2))/3,10*(sin($a)+sin($a+$a1)+sin($a+$a2))/3
goal_text=trouver le barycentre du triangle 1 2 3
hint=Le barycentre d'un triangle est le point commun des trois droites,\
chacune joignant un sommet et le milieu du ct oppos. Comme ces trois\
droites passent par un mme point, il vous suffit d'en tracer deux, puis\
marquer l'intersection.
solution=middle,1,2\
middle,1,3\
middle,2,3\
segment,1,6\
segment,2,5\
segment,3,4\
point,line,4,line,5

