Construction in GCLC language

dim 120 120

point A 80 95
point E_{a} 80 83.86
point O 65 51.14

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{a}
cmark_t O
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 point N such that ON/OH=0.5
towards N O H 0.5 
cmark_r N
color 200 200 200
drawsegment O H 
color 0 0 0



% Constructing a line L_{\_G14099} which passes through point O and point H
line L_{\_G14099} O H 

color 200 200 200
drawline L_{\_G14099}
color 0 0 0


% Constructing a point P_{\_G14200} with coordinates (0,0)
point P_{\_G14200} 0 0 
cmark_r P_{\_G14200}

% Constructing a point P_{\_G14124} such that OP_{\_G14124}/OP_{\_G14200}=1
towards P_{\_G14124} O P_{\_G14200} 1 
cmark_r P_{\_G14124}
color 200 200 200
drawsegment O P_{\_G14124} 
color 0 0 0

% Constructing a point P_{\_G14169} such that OP_{\_G14169}/OP_{\_G14200}=3
towards P_{\_G14169} O P_{\_G14200} 3 
cmark_r P_{\_G14169}
color 200 200 200
drawsegment O P_{\_G14169} 
color 0 0 0

% Constructing a line L_{\_G14130} which passes through point H and point P_{\_G14169}
line L_{\_G14130} H P_{\_G14169} 

color 200 200 200
drawline L_{\_G14130}
color 0 0 0


% Constructing a line L_{\_G14093} which contains the point P_{\_G14124} and is parallel to the line L_{\_G14130}
parallel L_{\_G14093} P_{\_G14124} L_{\_G14130} 

color 200 200 200
drawline L_{\_G14093}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G14093} and line L_{\_G14099}
intersec G L_{\_G14093} L_{\_G14099} 
cmark_t G



% Constructing a point M_{a} such that AM_{a}/AG=1.5
towards M_{a} A G 1.5 
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a} 
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_{\_G15087} which is a foot of the point N on the line h_{a}
foot P_{\_G15087} N h_{a} 
cmark_r P_{\_G15087}
color 200 200 200
drawline N P_{\_G15087} 
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_{\_G15087}
sim H_{a} P_{\_G15087} 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