Construction in GCLC language

dim 120 120

point M_{a} 65 40
point M_{c} 50 67.5
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

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

% NDG:  points H_{b} 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_{b}
circle k(M_{a},B) M_{a} H_{b} 

color 200 200 200
drawcircle k(M_{a},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:  circles k(M_{a},B) and k(M_{c},A) intersect% DET:  circles k(M_{a},B) and k(M_{c},A) are not the same; points H_{b} and B must be different
% Constructing a line L_{\_G44216} which passes through point M_{a} and point M_{c}
line L_{\_G44216} M_{a} M_{c} 

color 200 200 200
drawline L_{\_G44216}
color 0 0 0


% Constructing a point B which is an image of the point H_{b} in the symmetry to point/line L_{\_G44216}
sim B L_{\_G44216} H_{b} 
cmark_b B



% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0



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