Construction in GCLC language

dim 120 120

point B 20 40
point C 110 40
point H 80 72.73

color 220 0 0
fontsize 11

cmark_b B
cmark_b C
cmark_rt H
color 0 0 0
fontsize 10


% Constructing a point M_{a} such that BM_{a}/BC=0.5
towards M_{a} B C 0.5 
cmark_b M_{a}
color 200 200 200
drawsegment B C 
color 0 0 0


% DET:  points B and H are not the same
% Constructing a line h_{b} which passes through point B and point H
line h_{b} B H 

color 200 200 200
drawline h_{b}
color 0 0 0



% DET:  points C and H are not the same
% Constructing a line h_{c} which passes through point C and point H
line h_{c} C H 

color 200 200 200
drawline h_{c}
color 0 0 0



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

color 200 200 200
drawcircle k(M_{a},B)
color 0 0 0



% NDG:  line h_{b} and circle k(M_{a},B) intersect% DET:  points B and H_{b} must be different
% Constructing a point P_{\_G18222} which is a foot of the point M_{a} on the line h_{b}
foot P_{\_G18222} M_{a} h_{b} 
cmark_r P_{\_G18222}
color 200 200 200
drawline M_{a} P_{\_G18222} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G18222}
sim H_{b} P_{\_G18222} B 
cmark_rt H_{b}


% 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:  line h_{c} and circle k(M_{a},B) intersect% DET:  points C and H_{c} must be different
% Constructing a point P_{\_G18460} which is a foot of the point M_{a} on the line h_{c}
foot P_{\_G18460} M_{a} h_{c} 
cmark_r P_{\_G18460}
color 200 200 200
drawline M_{a} P_{\_G18460} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G18460}
sim H_{c} P_{\_G18460} C 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  lines b and c are not parallel% DET:  lines b and c are not the same
% Constructing a point A which belongs to line b and line c
intersec A b c 
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

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