Construction in GCLC language

dim 120 120

point M_{a} 65 40
point N 72.5 61.93
point O 65 51.14

color 220 0 0
fontsize 11

cmark_b M_{a}
cmark_r N
cmark_t O
color 0 0 0
fontsize 10


% Constructing a line L_{\_G107063} which passes through point N and point O
line L_{\_G107063} N O 

color 200 200 200
drawline L_{\_G107063}
color 0 0 0


% Constructing a point P_{\_G107164} with coordinates (0,0)
point P_{\_G107164} 0 0 
cmark_r P_{\_G107164}

% Constructing a point P_{\_G107088} such that NP_{\_G107088}/NP_{\_G107164}=1
towards P_{\_G107088} N P_{\_G107164} 1 
cmark_r P_{\_G107088}
color 200 200 200
drawsegment N P_{\_G107088} 
color 0 0 0

% Constructing a point P_{\_G107133} such that NP_{\_G107133}/NP_{\_G107164}=3
towards P_{\_G107133} N P_{\_G107164} 3 
cmark_r P_{\_G107133}
color 200 200 200
drawsegment N P_{\_G107133} 
color 0 0 0

% Constructing a line L_{\_G107094} which passes through point O and point P_{\_G107133}
line L_{\_G107094} O P_{\_G107133} 

color 200 200 200
drawline L_{\_G107094}
color 0 0 0


% Constructing a line L_{\_G107057} which contains the point P_{\_G107088} and is parallel to the line L_{\_G107094}
parallel L_{\_G107057} P_{\_G107088} L_{\_G107094} 

color 200 200 200
drawline L_{\_G107057}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G107057} and line L_{\_G107063}
intersec G L_{\_G107057} L_{\_G107063} 
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 H such that NH/NO=-1
towards H N O -1 
cmark_rt H
color 200 200 200
drawsegment O H 
color 0 0 0



% Constructing a point E_{a} such that AE_{a}/AH=0.5
towards E_{a} A H 0.5 
cmark_r E_{a}
color 200 200 200
drawsegment A H 
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:  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_{\_G108148} which is a foot of the point N on the line h_{a}
foot P_{\_G108148} N h_{a} 
cmark_r P_{\_G108148}
color 200 200 200
drawline N P_{\_G108148} 
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_{\_G108148}
sim H_{a} P_{\_G108148} 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 A and H are not the same