Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point H 80 72.73

color 220 0 0
fontsize 11

cmark_lt H_{c}
cmark_rt H
color 0 0 0
fontsize 10


% point B is given by the problem setting, but it has to belong to the line c which is constructible from the others objects given 
% DET:  points H_{c} and H are not the same
% Constructing a line h_{c} which passes through point H_{c} and point H
line h_{c} H_{c} H 

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




% Constructing a line c which is perpendicular to line h_{c} and which passes through point H_{c}
perp c H_{c} h_{c} 

color 200 200 200
drawline c
color 0 0 0




% Constructing a point P_{\_G36272} with coordinates (10,30)
point P_{\_G36272} 10 30 
cmark_r P_{\_G36272}

% Constructing a line L_{\_G36275} which passes through point H and point H_{c}
line L_{\_G36275} H H_{c} 

color 200 200 200
drawline L_{\_G36275}
color 0 0 0


% Constructing a line L_{\_G36278} which is perpendicular to line L_{\_G36275} and which passes through point H_{c}
perp L_{\_G36278} H_{c} L_{\_G36275} 

color 200 200 200
drawline L_{\_G36278}
color 0 0 0


% Constructing a line L_{\_G36281} which passes through point H and point P_{\_G36272}
line L_{\_G36281} H P_{\_G36272} 

color 200 200 200
drawline L_{\_G36281}
color 0 0 0


% Constructing a point B which belongs to line L_{\_G36281} and line L_{\_G36278}
intersec B L_{\_G36281} L_{\_G36278} 
color 220 0 0
fontsize 11
cmark_b B
color 0 0 0
fontsize 10



% 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




% Constructing a point A such that BA/BH_{c}=0.8526927612370688
towards A B H_{c} 0.8526927612370688 
cmark_t A
color 200 200 200
drawsegment B H_{c} 
color 0 0 0



% Constructing a point M_{c} such that AM_{c}/AB=0.5
towards M_{c} A B 0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment A B 
color 0 0 0


% NDG:  points 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 A
circle k(M_{c},A) M_{c} A 

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line h_{b} and circle k(M_{c},A) intersect% DET:  points B and H_{b} must be different
% Constructing a point P_{\_G36961} which is a foot of the point M_{c} on the line h_{b}
foot P_{\_G36961} M_{c} h_{b} 
cmark_r P_{\_G36961}
color 200 200 200
drawline M_{c} P_{\_G36961} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G36961}
sim H_{b} P_{\_G36961} B 
cmark_rt H_{b}


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  lines h_{c} and b are not parallel% DET:  lines h_{c} and b are not the same
% Constructing a point C which belongs to line h_{c} and line b
intersec C h_{c} b 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

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