Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point G 70 58.33
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_lt M_{c}
cmark_t G
cmark_b H_{a}
color 0 0 0
fontsize 10


% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0


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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line a and circle k(M_{c},A) intersect% DET:  points H_{a} and B must be different
% Constructing a point P_{\_G52707} which is a foot of the point M_{c} on the line a
foot P_{\_G52707} M_{c} a 
cmark_r P_{\_G52707}
color 200 200 200
drawline M_{c} P_{\_G52707} 
color 0 0 0

% Constructing a point B which is an image of the point H_{a} in the symmetry to point/line P_{\_G52707}
sim B P_{\_G52707} H_{a} 
cmark_b B



% Constructing a point A such that BA/BM_{c}=2
towards A B M_{c} 2 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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