Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point M_{c} 50 67.5
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_lt M_{c}
cmark_b H_{a}
color 0 0 0
fontsize 10

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

color 200 200 200
drawcircle k(M_{b},C)
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:  circles k(M_{b},C) and k(M_{c},A) intersect% DET:  circles k(M_{b},C) and k(M_{c},A) are not the same; points H_{a} and A must be different
% Constructing a line L_{\_G60530} which passes through point M_{b} and point M_{c}
line L_{\_G60530} M_{b} M_{c} 

color 200 200 200
drawline L_{\_G60530}
color 0 0 0


% Constructing a point A which is an image of the point H_{a} in the symmetry to point/line L_{\_G60530}
sim A L_{\_G60530} H_{a} 
cmark_t A



% 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



% Constructing a point B such that M_{c}B/M_{c}A=-1
towards B M_{c} A -1 
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:  circles k(M_{b},C) and k(M_{c},A) intersect; points H_{a} and M_{c} are not the same; points H_{a} and M_{b} are not the same
% Determination conditions:  circles k(M_{b},C) and k(M_{c},A) are not the same; points H_{a} and A must be different