Construction in GCLC language

dim 120 120

point A 80 95
point G 70 58.33
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_t A
cmark_t G
cmark_lt H_{c}
color 0 0 0
fontsize 10


% Constructing a point M_{a} such that AM_{a}/AG=1.5
towards M_{a} A G 1.5 
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a} 
color 0 0 0


% DET:  points A and H_{c} are not the same
% Constructing a line c which passes through point A and point H_{c}
line c A H_{c} 

color 200 200 200
drawline c
color 0 0 0



% NDG:  points H_{c} and M_{a} are not the same
% Constructing a circle k(M_{a},B) whose center is at point M_{a} and which passes through point H_{c}
circle k(M_{a},B) M_{a} H_{c} 

color 200 200 200
drawcircle k(M_{a},B)
color 0 0 0



% NDG:  line c and circle k(M_{a},B) intersect% DET:  points H_{c} and B must be different
% Constructing a point P_{\_G14415} which is a foot of the point M_{a} on the line c
foot P_{\_G14415} M_{a} c 
cmark_r P_{\_G14415}
color 200 200 200
drawline M_{a} P_{\_G14415} 
color 0 0 0

% Constructing a point B which is an image of the point H_{c} in the symmetry to point/line P_{\_G14415}
sim B P_{\_G14415} H_{c} 
cmark_b B



% Constructing a point M_{b} such that GM_{b}/GB=-0.5
towards M_{b} G B -0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b} 
color 0 0 0



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line c and circle k(M_{a},B) intersect; points H_{c} and M_{a} are not the same
% Determination conditions:  points H_{c} and B must be different; points A and H_{c} are not the same