Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point G 70 58.33
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_t G
cmark_rt H_{b}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline h_{b}
color 0 0 0




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

color 200 200 200
drawline b
color 0 0 0




% Constructing a point P_{\_G30996} such that GP_{\_G30996}/GE_{b}=-0.5
towards P_{\_G30996} G E_{b} -0.5 
cmark_r P_{\_G30996}
color 200 200 200
drawsegment E_{b} P_{\_G30996} 
color 0 0 0

% Constructing a line h_{G,-1/2}(h_{b}) which contains the point P_{\_G30996} and is parallel to the line h_{b}
parallel h_{G,-1/2}(h_{b}) P_{\_G30996} h_{b} 

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



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



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



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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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