Construction in GCLC language

dim 120 120

point A 80 95
point E_{a} 80 83.86
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{a}
cmark_b M_{a}
color 0 0 0
fontsize 10


% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0



% Constructing a line L_{\_G5349} which passes through point A and point M_{a}
line L_{\_G5349} A M_{a} 

color 200 200 200
drawline L_{\_G5349}
color 0 0 0


% Constructing a point P_{\_G5450} with coordinates (0,0)
point P_{\_G5450} 0 0 
cmark_r P_{\_G5450}

% Constructing a point P_{\_G5374} such that AP_{\_G5374}/AP_{\_G5450}=2
towards P_{\_G5374} A P_{\_G5450} 2 
cmark_r P_{\_G5374}
color 200 200 200
drawsegment A P_{\_G5374} 
color 0 0 0

% Constructing a point P_{\_G5419} such that AP_{\_G5419}/AP_{\_G5450}=3
towards P_{\_G5419} A P_{\_G5450} 3 
cmark_r P_{\_G5419}
color 200 200 200
drawsegment A P_{\_G5419} 
color 0 0 0

% Constructing a line L_{\_G5380} which passes through point M_{a} and point P_{\_G5419}
line L_{\_G5380} M_{a} P_{\_G5419} 

color 200 200 200
drawline L_{\_G5380}
color 0 0 0


% Constructing a line L_{\_G5343} which contains the point P_{\_G5374} and is parallel to the line L_{\_G5380}
parallel L_{\_G5343} P_{\_G5374} L_{\_G5380} 

color 200 200 200
drawline L_{\_G5343}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G5343} and line L_{\_G5349}
intersec G L_{\_G5343} L_{\_G5349} 
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 A and E_{a} are not the same
% Constructing a line h_{a} which passes through point A and point E_{a}
line h_{a} A E_{a} 

color 200 200 200
drawline h_{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:  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_{\_G6420} which is a foot of the point N on the line h_{a}
foot P_{\_G6420} N h_{a} 
cmark_r P_{\_G6420}
color 200 200 200
drawline N P_{\_G6420} 
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_{\_G6420}
sim H_{a} P_{\_G6420} 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:  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; line h_{a} and circle k(N,M_{a}) intersect; points E_{a} and N are not the same; points A and O 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 A and E_{a} are not the same