Construction in GCLC language

dim 120 120

point H 80 72.73
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_rt H
cmark_b H_{a}
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}(a) which is constructible from the others objects given 
% DET:  points H and H_{a} are not the same
% Constructing a line h_{a} which passes through point H and point H_{a}
line h_{a} H H_{a} 

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




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

color 200 200 200
drawline a
color 0 0 0




% Constructing a point P_{\_G30117} such that HP_{\_G30117}/HH_{a}=0.5
towards P_{\_G30117} H H_{a} 0.5 
cmark_r P_{\_G30117}
color 200 200 200
drawsegment H H_{a} 
color 0 0 0

% Constructing a line h_{H,1/2}(a) which contains the point P_{\_G30117} and is parallel to the line a
parallel h_{H,1/2}(a) P_{\_G30117} a 

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




% Constructing a point P_{\_G30475} such that HP_{\_G30475}/HH_{a}=0.5
towards P_{\_G30475} H H_{a} 0.5 
cmark_r P_{\_G30475}
color 200 200 200
drawsegment H H_{a} 
color 0 0 0

% Constructing a point P_{\_G30478} with coordinates (10,30)
point P_{\_G30478} 10 30 
cmark_r P_{\_G30478}

% Constructing a line L_{\_G30481} which passes through point H and point P_{\_G30475}
line L_{\_G30481} H P_{\_G30475} 

color 200 200 200
drawline L_{\_G30481}
color 0 0 0


% Constructing a line L_{\_G30484} which is perpendicular to line L_{\_G30481} and which passes through point P_{\_G30475}
perp L_{\_G30484} P_{\_G30475} L_{\_G30481} 

color 200 200 200
drawline L_{\_G30484}
color 0 0 0


% Constructing a line L_{\_G30487} which passes through point H and point P_{\_G30478}
line L_{\_G30487} H P_{\_G30478} 

color 200 200 200
drawline L_{\_G30487}
color 0 0 0


% Constructing a point E_{b} which belongs to line L_{\_G30487} and line L_{\_G30484}
intersec E_{b} L_{\_G30487} L_{\_G30484} 
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 HA/HH_{a}=0.3483591850015648
towards A H H_{a} 0.3483591850015648 
cmark_t A
color 200 200 200
drawsegment H H_{a} 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  line c and circle k(E_{b},B) intersect% DET:  points B and H_{c} must be different
% Constructing a point P_{\_G31262} which is a foot of the point E_{b} on the line c
foot P_{\_G31262} E_{b} c 
cmark_r P_{\_G31262}
color 200 200 200
drawline E_{b} P_{\_G31262} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point B in the symmetry to point/line P_{\_G31262}
sim H_{c} P_{\_G31262} B 
cmark_lt H_{c}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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