Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point G 70 58.33
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_t G
cmark_b H_{a}
color 0 0 0
fontsize 10

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

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




% Constructing a line a which is perpendicular to line h_{a} and which passes through point H_{a}
perp a H_{a} h_{a} 

color 200 200 200
drawline a
color 0 0 0




% Constructing a point P_{\_G25141} such that GP_{\_G25141}/GE_{a}=-0.5
towards P_{\_G25141} G E_{a} -0.5 
cmark_r P_{\_G25141}
color 200 200 200
drawsegment E_{a} P_{\_G25141} 
color 0 0 0

% Constructing a line h_{G,-1/2}(h_{a}) which contains the point P_{\_G25141} and is parallel to the line h_{a}
parallel h_{G,-1/2}(h_{a}) P_{\_G25141} h_{a} 

color 200 200 200
drawline h_{G,-1/2}(h_{a})
color 0 0 0



% NDG:  lines h_{G,-1/2}(h_{a}) and a are not parallel% DET:  lines h_{G,-1/2}(h_{a}) and a are not the same
% Constructing a point M_{a} which belongs to line h_{G,-1/2}(h_{a}) and line a
intersec M_{a} h_{G,-1/2}(h_{a}) a 
cmark_b M_{a}



% 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 E_{a}H/E_{a}A=-1
towards H E_{a} A -1 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0



% Constructing a point O such that GO/GH=-0.5
towards O G H -0.5 
cmark_t O
color 200 200 200
drawsegment H O 
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; lines h_{G,-1/2}(h_{a}) and a are not parallel
% Determination conditions:  lines h_{G,-1/2}(h_{a}) and a are not the same; points E_{a} and H_{a} are not the same