Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_lt H_{c}
color 0 0 0
fontsize 10


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

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




% Constructing a point C such that E_{c}C/E_{c}H_{c}=0.5321995277264081
towards C E_{c} H_{c} 0.5321995277264081 
color 220 0 0
fontsize 11
cmark_b C
color 0 0 0
fontsize 10

color 200 200 200
drawsegment E_{c} H_{c} 
color 0 0 0



% Constructing a point H such that CH/CE_{c}=2
towards H C E_{c} 2 
cmark_rt H
color 200 200 200
drawsegment C H 
color 0 0 0


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

color 200 200 200
drawcircle k(E_{c},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_{\_G30600} with coordinates (10,30)
point P_{\_G30600} 10 30 
cmark_r P_{\_G30600}

% Constructing a line L_{\_G30603} which passes through point C and point H_{c}
line L_{\_G30603} C H_{c} 

color 200 200 200
drawline L_{\_G30603}
color 0 0 0


% Constructing a line L_{\_G30606} which is perpendicular to line L_{\_G30603} and which passes through point H_{c}
perp L_{\_G30606} H_{c} L_{\_G30603} 

color 200 200 200
drawline L_{\_G30606}
color 0 0 0


% Constructing a line L_{\_G30609} which passes through point C and point P_{\_G30600}
line L_{\_G30609} C P_{\_G30600} 

color 200 200 200
drawline L_{\_G30609}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G30609} and line L_{\_G30606}
intersec A L_{\_G30609} L_{\_G30606} 
cmark_t A


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  line b and circle k(E_{c},C) intersect% DET:  points C and H_{b} must be different
% Constructing a point P_{\_G31010} which is a foot of the point E_{c} on the line b
foot P_{\_G31010} E_{c} b 
cmark_r P_{\_G31010}
color 200 200 200
drawline E_{c} P_{\_G31010} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point C in the symmetry to point/line P_{\_G31010}
sim H_{b} P_{\_G31010} C 
cmark_rt H_{b}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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