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 C 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_{\_G49367} with coordinates (10,30)
point P_{\_G49367} 10 30 
cmark_r P_{\_G49367}

% Constructing a line L_{\_G49370} which passes through point H and point H_{b}
line L_{\_G49370} H H_{b} 

color 200 200 200
drawline L_{\_G49370}
color 0 0 0


% Constructing a line L_{\_G49373} which is perpendicular to line L_{\_G49370} and which passes through point H_{b}
perp L_{\_G49373} H_{b} L_{\_G49370} 

color 200 200 200
drawline L_{\_G49373}
color 0 0 0


% Constructing a line L_{\_G49376} which passes through point H and point P_{\_G49367}
line L_{\_G49376} H P_{\_G49367} 

color 200 200 200
drawline L_{\_G49376}
color 0 0 0


% Constructing a point C which belongs to line L_{\_G49376} and line L_{\_G49373}
intersec C L_{\_G49376} L_{\_G49373} 
color 220 0 0
fontsize 11
cmark_b C
color 0 0 0
fontsize 10



% 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




% Constructing a point A such that CA/CH_{b}=0.23110648136144124
towards A C H_{b} 0.23110648136144124 
cmark_t A
color 200 200 200
drawsegment C H_{b} 
color 0 0 0



% Constructing a point M_{b} such that AM_{b}/AC=0.5
towards M_{b} A C 0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment A C 
color 0 0 0


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

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



% NDG:  line h_{c} and circle k(M_{b},C) intersect% DET:  points C and H_{c} must be different
% Constructing a point P_{\_G50056} which is a foot of the point M_{b} on the line h_{c}
foot P_{\_G50056} M_{b} h_{c} 
cmark_r P_{\_G50056}
color 200 200 200
drawline M_{b} P_{\_G50056} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G50056}
sim H_{c} P_{\_G50056} C 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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