Construction in GCLC language

dim 120 120

point H 80 72.73
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_rt H
cmark_rt H_{b}
color 0 0 0
fontsize 10


% point E_{a} is given by the problem setting, but it has to belong to the line h_{H,1/2}(b) which is constructible from the others objects given 
% 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




% 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_{\_G48731} such that HP_{\_G48731}/HH_{b}=0.5
towards P_{\_G48731} H H_{b} 0.5 
cmark_r P_{\_G48731}
color 200 200 200
drawsegment H H_{b} 
color 0 0 0

% Constructing a line h_{H,1/2}(b) which contains the point P_{\_G48731} and is parallel to the line b
parallel h_{H,1/2}(b) P_{\_G48731} b 

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




% Constructing a point P_{\_G49089} such that HP_{\_G49089}/HH_{b}=0.5
towards P_{\_G49089} H H_{b} 0.5 
cmark_r P_{\_G49089}
color 200 200 200
drawsegment H H_{b} 
color 0 0 0

% Constructing a point P_{\_G49092} with coordinates (10,30)
point P_{\_G49092} 10 30 
cmark_r P_{\_G49092}

% Constructing a line L_{\_G49095} which passes through point H and point P_{\_G49089}
line L_{\_G49095} H P_{\_G49089} 

color 200 200 200
drawline L_{\_G49095}
color 0 0 0


% Constructing a line L_{\_G49098} which is perpendicular to line L_{\_G49095} and which passes through point P_{\_G49089}
perp L_{\_G49098} P_{\_G49089} L_{\_G49095} 

color 200 200 200
drawline L_{\_G49098}
color 0 0 0


% Constructing a line L_{\_G49101} which passes through point H and point P_{\_G49092}
line L_{\_G49101} H P_{\_G49092} 

color 200 200 200
drawline L_{\_G49101}
color 0 0 0


% Constructing a point E_{a} which belongs to line L_{\_G49101} and line L_{\_G49098}
intersec E_{a} L_{\_G49101} L_{\_G49098} 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10




% Constructing a point A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0


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

color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0




% Constructing a point B such that HB/HH_{b}=0.8711604592993983
towards B H H_{b} 0.8711604592993983 
cmark_b B
color 200 200 200
drawsegment H H_{b} 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  line c and circle k(E_{a},A) intersect% DET:  points A and H_{c} must be different
% Constructing a point P_{\_G49876} which is a foot of the point E_{a} on the line c
foot P_{\_G49876} E_{a} c 
cmark_r P_{\_G49876}
color 200 200 200
drawline E_{a} P_{\_G49876} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point A in the symmetry to point/line P_{\_G49876}
sim H_{c} P_{\_G49876} A 
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 b and h_{c} are not parallel% DET:  lines b and h_{c} are not the same
% Constructing a point C which belongs to line b and line h_{c}
intersec C b h_{c} 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

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