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_{c} 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_{\_G49218} such that HP_{\_G49218}/HH_{b}=0.5
towards P_{\_G49218} H H_{b} 0.5 
cmark_r P_{\_G49218}
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_{\_G49218} and is parallel to the line b
parallel h_{H,1/2}(b) P_{\_G49218} b 

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




% Constructing a point P_{\_G49576} such that HP_{\_G49576}/HH_{b}=0.5
towards P_{\_G49576} H H_{b} 0.5 
cmark_r P_{\_G49576}
color 200 200 200
drawsegment H H_{b} 
color 0 0 0

% Constructing a point P_{\_G49579} with coordinates (10,30)
point P_{\_G49579} 10 30 
cmark_r P_{\_G49579}

% Constructing a line L_{\_G49582} which passes through point H and point P_{\_G49576}
line L_{\_G49582} H P_{\_G49576} 

color 200 200 200
drawline L_{\_G49582}
color 0 0 0


% Constructing a line L_{\_G49585} which is perpendicular to line L_{\_G49582} and which passes through point P_{\_G49576}
perp L_{\_G49585} P_{\_G49576} L_{\_G49582} 

color 200 200 200
drawline L_{\_G49585}
color 0 0 0


% Constructing a line L_{\_G49588} which passes through point H and point P_{\_G49579}
line L_{\_G49588} H P_{\_G49579} 

color 200 200 200
drawline L_{\_G49588}
color 0 0 0


% Constructing a point E_{c} which belongs to line L_{\_G49588} and line L_{\_G49585}
intersec E_{c} L_{\_G49588} L_{\_G49585} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10




% 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 point A such that H_{b}A/H_{b}C=0.5090308176688207
towards A H_{b} C 0.5090308176688207 
cmark_t A
color 200 200 200
drawsegment H_{b} C 
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_{c},C) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G50363} which is a foot of the point E_{c} on the line h_{a}
foot P_{\_G50363} E_{c} h_{a} 
cmark_r P_{\_G50363}
color 200 200 200
drawline E_{c} P_{\_G50363} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G50363}
sim H_{a} P_{\_G50363} 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 h_{b} and a are not parallel% DET:  lines h_{b} and a are not the same
% Constructing a point B which belongs to line h_{b} and line a
intersec B h_{b} a 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines h_{b} 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 h_{b} 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_{b} are not the same