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_{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 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 point E_{c} such that HE_{c}/HH_{c}=0.9883625815716551
towards E_{c} H H_{c} 0.9883625815716551 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10

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



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


% NDG:  points H 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 H
circle k(E_{c},C) E_{c} H 

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_{\_G54085} with coordinates (10,30)
point P_{\_G54085} 10 30 
cmark_r P_{\_G54085}

% Constructing a line L_{\_G54088} which passes through point E_{c} and point H_{c}
line L_{\_G54088} E_{c} H_{c} 

color 200 200 200
drawline L_{\_G54088}
color 0 0 0


% Constructing a line L_{\_G54091} which is perpendicular to line L_{\_G54088} and which passes through point H_{c}
perp L_{\_G54091} H_{c} L_{\_G54088} 

color 200 200 200
drawline L_{\_G54091}
color 0 0 0


% Constructing a line L_{\_G54094} which passes through point E_{c} and point P_{\_G54085}
line L_{\_G54094} E_{c} P_{\_G54085} 

color 200 200 200
drawline L_{\_G54094}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G54094} and line L_{\_G54091}
intersec A L_{\_G54094} L_{\_G54091} 
cmark_t A


% 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_{c},C) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G54495} which is a foot of the point E_{c} on the line h_{a}
foot P_{\_G54495} E_{c} h_{a} 
cmark_r P_{\_G54495}
color 200 200 200
drawline E_{c} P_{\_G54495} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G54495}
sim H_{a} P_{\_G54495} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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