Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H 80 72.73
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_rt H
cmark_b M_{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



% Constructing a line L_{\_G32807} which passes through point M_{a} and point A
line L_{\_G32807} M_{a} A 

color 200 200 200
drawline L_{\_G32807}
color 0 0 0


% Constructing a point P_{\_G32908} with coordinates (0,0)
point P_{\_G32908} 0 0 
cmark_r P_{\_G32908}

% Constructing a point P_{\_G32832} such that M_{a}P_{\_G32832}/M_{a}P_{\_G32908}=1
towards P_{\_G32832} M_{a} P_{\_G32908} 1 
cmark_r P_{\_G32832}
color 200 200 200
drawsegment M_{a} P_{\_G32832} 
color 0 0 0

% Constructing a point P_{\_G32877} such that M_{a}P_{\_G32877}/M_{a}P_{\_G32908}=3
towards P_{\_G32877} M_{a} P_{\_G32908} 3 
cmark_r P_{\_G32877}
color 200 200 200
drawsegment M_{a} P_{\_G32877} 
color 0 0 0

% Constructing a line L_{\_G32838} which passes through point A and point P_{\_G32877}
line L_{\_G32838} A P_{\_G32877} 

color 200 200 200
drawline L_{\_G32838}
color 0 0 0


% Constructing a line L_{\_G32801} which contains the point P_{\_G32832} and is parallel to the line L_{\_G32838}
parallel L_{\_G32801} P_{\_G32832} L_{\_G32838} 

color 200 200 200
drawline L_{\_G32801}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G32801} and line L_{\_G32807}
intersec G L_{\_G32801} L_{\_G32807} 
cmark_t G



% Constructing a point N such that HN/HG=0.75
towards N H G 0.75 
cmark_r N
color 200 200 200
drawsegment H G 
color 0 0 0



% Constructing a point O such that HO/HG=1.5
towards O H G 1.5 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0


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

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



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

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line h_{a} and circle k(N,M_{a}) intersect% DET:  points E_{a} and H_{a} must be different
% Constructing a point P_{\_G33827} which is a foot of the point N on the line h_{a}
foot P_{\_G33827} N h_{a} 
cmark_r P_{\_G33827}
color 200 200 200
drawline N P_{\_G33827} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point E_{a} in the symmetry to point/line P_{\_G33827}
sim H_{a} P_{\_G33827} E_{a} 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line a and circle k(O,C) intersect
% Constructing points C and B which are in intersection of k(O,C) and a
intersec2 C B k(O,C) a 
cmark_b C
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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