Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point G 70 58.33
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_t G
cmark_lt H_{c}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline h_{c}
color 0 0 0




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

color 200 200 200
drawline c
color 0 0 0




% Constructing a point P_{\_G63753} such that GP_{\_G63753}/GE_{c}=-0.5
towards P_{\_G63753} G E_{c} -0.5 
cmark_r P_{\_G63753}
color 200 200 200
drawsegment E_{c} P_{\_G63753} 
color 0 0 0

% Constructing a line h_{G,-1/2}(h_{c}) which contains the point P_{\_G63753} and is parallel to the line h_{c}
parallel h_{G,-1/2}(h_{c}) P_{\_G63753} h_{c} 

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



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



% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0



% Constructing a point H such that E_{c}H/E_{c}C=-1
towards H E_{c} C -1 
cmark_rt H
color 200 200 200
drawsegment C 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 C and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point C
circle k(O,C) O C 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line c and circle k(O,C) intersect
% Constructing points A and B which are in intersection of k(O,C) and c
intersec2 A B k(O,C) c 
cmark_t A
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line c and circle k(O,C) intersect; points C and O are not the same; lines h_{G,-1/2}(h_{c}) and c are not parallel
% Determination conditions:  lines h_{G,-1/2}(h_{c}) and c are not the same; points E_{c} and H_{c} are not the same