Construction in GCLC language

dim 120 120

point H 80 72.73
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

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


% point E_{b} is given by the problem setting, but it has to belong to the line h_{H,1/2}(c) which is constructible from the others objects given 
% DET:  points H and H_{c} are not the same
% Constructing a line h_{c} which passes through point H and point H_{c}
line h_{c} H H_{c} 

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_{\_G59996} such that HP_{\_G59996}/HH_{c}=0.5
towards P_{\_G59996} H H_{c} 0.5 
cmark_r P_{\_G59996}
color 200 200 200
drawsegment H H_{c} 
color 0 0 0

% Constructing a line h_{H,1/2}(c) which contains the point P_{\_G59996} and is parallel to the line c
parallel h_{H,1/2}(c) P_{\_G59996} c 

color 200 200 200
drawline h_{H,1/2}(c)
color 0 0 0




% Constructing a point P_{\_G60354} such that HP_{\_G60354}/HH_{c}=0.5
towards P_{\_G60354} H H_{c} 0.5 
cmark_r P_{\_G60354}
color 200 200 200
drawsegment H H_{c} 
color 0 0 0

% Constructing a point P_{\_G60357} with coordinates (10,30)
point P_{\_G60357} 10 30 
cmark_r P_{\_G60357}

% Constructing a line L_{\_G60360} which passes through point H and point P_{\_G60354}
line L_{\_G60360} H P_{\_G60354} 

color 200 200 200
drawline L_{\_G60360}
color 0 0 0


% Constructing a line L_{\_G60363} which is perpendicular to line L_{\_G60360} and which passes through point P_{\_G60354}
perp L_{\_G60363} P_{\_G60354} L_{\_G60360} 

color 200 200 200
drawline L_{\_G60363}
color 0 0 0


% Constructing a line L_{\_G60366} which passes through point H and point P_{\_G60357}
line L_{\_G60366} H P_{\_G60357} 

color 200 200 200
drawline L_{\_G60366}
color 0 0 0


% Constructing a point E_{b} which belongs to line L_{\_G60366} and line L_{\_G60363}
intersec E_{b} L_{\_G60366} L_{\_G60363} 
color 220 0 0
fontsize 11
cmark_r E_{b}
color 0 0 0
fontsize 10




% Constructing a point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0


% NDG:  points H and E_{b} are not the same
% Constructing a circle k(E_{b},B) whose center is at point E_{b} and which passes through point H
circle k(E_{b},B) E_{b} H 

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0




% Constructing a point A such that H_{c}A/H_{c}B=0.7406051182808979
towards A H_{c} B 0.7406051182808979 
cmark_t A
color 200 200 200
drawsegment H_{c} B 
color 0 0 0


% 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



% NDG:  line h_{a} and circle k(E_{b},B) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G61141} which is a foot of the point E_{b} on the line h_{a}
foot P_{\_G61141} E_{b} h_{a} 
cmark_r P_{\_G61141}
color 200 200 200
drawline E_{b} P_{\_G61141} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G61141}
sim H_{a} P_{\_G61141} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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