Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point G 70 58.33
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_lt M_{c}
cmark_t G
cmark_rt H_{b}
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_{b} and C are not the same
% Constructing a line b which passes through point H_{b} and point C
line b H_{b} C 

color 200 200 200
drawline b
color 0 0 0



% NDG:  points H_{b} 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_{b}
circle k(M_{c},A) M_{c} H_{b} 

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



% NDG:  line b and circle k(M_{c},A) intersect% DET:  points H_{b} and A must be different
% Constructing a point P_{\_G49060} which is a foot of the point M_{c} on the line b
foot P_{\_G49060} M_{c} b 
cmark_r P_{\_G49060}
color 200 200 200
drawline M_{c} P_{\_G49060} 
color 0 0 0

% Constructing a point A which is an image of the point H_{b} in the symmetry to point/line P_{\_G49060}
sim A P_{\_G49060} H_{b} 
cmark_t A



% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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