Construction in GCLC language

dim 120 120

point H 80 72.73
point M_{a} 65 40
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H
cmark_b M_{a}
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point O such that HO/HN=2
towards O H N 2 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0



% Constructing a line L_{\_G47977} which passes through point H and point N
line L_{\_G47977} H N 

color 200 200 200
drawline L_{\_G47977}
color 0 0 0


% Constructing a point P_{\_G48078} with coordinates (0,0)
point P_{\_G48078} 0 0 
cmark_r P_{\_G48078}

% Constructing a point P_{\_G48002} such that HP_{\_G48002}/HP_{\_G48078}=4
towards P_{\_G48002} H P_{\_G48078} 4 
cmark_r P_{\_G48002}
color 200 200 200
drawsegment H P_{\_G48002} 
color 0 0 0

% Constructing a point P_{\_G48047} such that HP_{\_G48047}/HP_{\_G48078}=3
towards P_{\_G48047} H P_{\_G48078} 3 
cmark_r P_{\_G48047}
color 200 200 200
drawsegment H P_{\_G48047} 
color 0 0 0

% Constructing a line L_{\_G48008} which passes through point N and point P_{\_G48047}
line L_{\_G48008} N P_{\_G48047} 

color 200 200 200
drawline L_{\_G48008}
color 0 0 0


% Constructing a line L_{\_G47971} which contains the point P_{\_G48002} and is parallel to the line L_{\_G48008}
parallel L_{\_G47971} P_{\_G48002} L_{\_G48008} 

color 200 200 200
drawline L_{\_G47971}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G47971} and line L_{\_G47977}
intersec G L_{\_G47971} L_{\_G47977} 
cmark_t G



% Constructing a point A such that M_{a}A/M_{a}G=3
towards A M_{a} G 3 
cmark_t A
color 200 200 200
drawsegment M_{a} A 
color 0 0 0



% Constructing a point E_{a} such that HE_{a}/HA=0.5
towards E_{a} H A 0.5 
cmark_r E_{a}
color 200 200 200
drawsegment H A 
color 0 0 0


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

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



% NDG:  points M_{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 M_{a}
circle k(N,M_{a}) N M_{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_{\_G48988} which is a foot of the point N on the line h_{a}
foot P_{\_G48988} N h_{a} 
cmark_r P_{\_G48988}
color 200 200 200
drawline N P_{\_G48988} 
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_{\_G48988}
sim H_{a} P_{\_G48988} 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 M_{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 H and A are not the same