Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point H 80 72.73

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_rt H
color 0 0 0
fontsize 10


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

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




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

color 200 200 200
drawline b
color 0 0 0




% Constructing a point P_{\_G23387} with coordinates (10,30)
point P_{\_G23387} 10 30 
cmark_r P_{\_G23387}

% Constructing a line L_{\_G23390} which passes through point H and point H_{b}
line L_{\_G23390} H H_{b} 

color 200 200 200
drawline L_{\_G23390}
color 0 0 0


% Constructing a line L_{\_G23393} which is perpendicular to line L_{\_G23390} and which passes through point H_{b}
perp L_{\_G23393} H_{b} L_{\_G23390} 

color 200 200 200
drawline L_{\_G23393}
color 0 0 0


% Constructing a line L_{\_G23396} which passes through point H and point P_{\_G23387}
line L_{\_G23396} H P_{\_G23387} 

color 200 200 200
drawline L_{\_G23396}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G23396} and line L_{\_G23393}
intersec A L_{\_G23396} L_{\_G23393} 
color 220 0 0
fontsize 11
cmark_t A
color 0 0 0
fontsize 10



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

color 200 200 200
drawline h_{a}
color 0 0 0




% Constructing a point B such that H_{b}B/H_{b}H=0.17069320925334028
towards B H_{b} H 0.17069320925334028 
cmark_b B
color 200 200 200
drawsegment H_{b} H 
color 0 0 0



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


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

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



% NDG:  line h_{a} and circle k(M_{c},A) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G24076} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G24076} M_{c} h_{a} 
cmark_r P_{\_G24076}
color 200 200 200
drawline M_{c} P_{\_G24076} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G24076}
sim H_{a} P_{\_G24076} A 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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