Construction in GCLC language

dim 120 120

point M_{a} 65 40
point M_{b} 95 67.5
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline b
color 0 0 0



% 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:  line b and circle k(M_{a},B) intersect% DET:  points H_{b} and C must be different
% Constructing a point P_{\_G62456} which is a foot of the point M_{a} on the line b
foot P_{\_G62456} M_{a} b 
cmark_r P_{\_G62456}
color 200 200 200
drawline M_{a} P_{\_G62456} 
color 0 0 0

% Constructing a point C which is an image of the point H_{b} in the symmetry to point/line P_{\_G62456}
sim C P_{\_G62456} H_{b} 
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:  line b and circle k(M_{a},B) intersect; points H_{b} and M_{a} are not the same
% Determination conditions:  points H_{b} and C must be different; points M_{b} and H_{b} are not the same