Construction in GCLC language

dim 120 120

point M_{a} 65 40
point M_{b} 95 67.5
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



% NDG:  circles k(M_{a},B) and k(M_{b},C) intersect% DET:  circles k(M_{a},B) and k(M_{b},C) are not the same; points H_{c} and C must be different
% Constructing a line L_{\_G49403} which passes through point M_{a} and point M_{b}
line L_{\_G49403} M_{a} M_{b} 

color 200 200 200
drawline L_{\_G49403}
color 0 0 0


% Constructing a point C which is an image of the point H_{c} in the symmetry to point/line L_{\_G49403}
sim C L_{\_G49403} H_{c} 
cmark_b C



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



% Constructing a point A such that M_{b}A/M_{b}C=-1
towards A M_{b} C -1 
cmark_t A
color 200 200 200
drawsegment C 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_{b},C) intersect; points H_{c} and M_{b} are not the same; points H_{c} and M_{a} are not the same
% Determination conditions:  circles k(M_{a},B) and k(M_{b},C) are not the same; points H_{c} and C must be different