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_{c} 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_{\_G39742} such that HP_{\_G39742}/HH_{a}=0.5
towards P_{\_G39742} H H_{a} 0.5 
cmark_r P_{\_G39742}
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_{\_G39742} and is parallel to the line a
parallel h_{H,1/2}(a) P_{\_G39742} a 

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




% Constructing a point P_{\_G40100} such that HP_{\_G40100}/HH_{a}=0.5
towards P_{\_G40100} H H_{a} 0.5 
cmark_r P_{\_G40100}
color 200 200 200
drawsegment H H_{a} 
color 0 0 0

% Constructing a point P_{\_G40103} with coordinates (10,30)
point P_{\_G40103} 10 30 
cmark_r P_{\_G40103}

% Constructing a line L_{\_G40106} which passes through point H and point P_{\_G40100}
line L_{\_G40106} H P_{\_G40100} 

color 200 200 200
drawline L_{\_G40106}
color 0 0 0


% Constructing a line L_{\_G40109} which is perpendicular to line L_{\_G40106} and which passes through point P_{\_G40100}
perp L_{\_G40109} P_{\_G40100} L_{\_G40106} 

color 200 200 200
drawline L_{\_G40109}
color 0 0 0


% Constructing a line L_{\_G40112} which passes through point H and point P_{\_G40103}
line L_{\_G40112} H P_{\_G40103} 

color 200 200 200
drawline L_{\_G40112}
color 0 0 0


% Constructing a point E_{c} which belongs to line L_{\_G40112} and line L_{\_G40109}
intersec E_{c} L_{\_G40112} L_{\_G40109} 
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 HA/HH_{a}=0.40189540995882145
towards A H H_{a} 0.40189540995882145 
cmark_t A
color 200 200 200
drawsegment H H_{a} 
color 0 0 0


% 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_{\_G40887} which is a foot of the point E_{c} on the line b
foot P_{\_G40887} E_{c} b 
cmark_r P_{\_G40887}
color 200 200 200
drawline E_{c} P_{\_G40887} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point C in the symmetry to point/line P_{\_G40887}
sim H_{b} P_{\_G40887} C 
cmark_rt H_{b}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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