Construction in GCLC language

dim 120 120

point O 65 51.14
point G 70 58.33
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_t O
cmark_t G
cmark_rt H_{b}
color 0 0 0
fontsize 10


% Constructing a point H such that OH/OG=3
towards H O G 3 
cmark_rt H
color 200 200 200
drawsegment O H 
color 0 0 0


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

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 line m_{b} which is perpendicular to line b and which passes through point O
perp m_{b} O b 

color 200 200 200
drawline m_{b}
color 0 0 0



% NDG:  lines m_{b} and b are not parallel% DET:  lines m_{b} and b are not the same
% Constructing a point M_{b} which belongs to line m_{b} and line b
intersec M_{b} m_{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


% 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 m_{b} and b are not parallel
% Determination conditions:  lines m_{b} and b are not the same; points H_{b} and H are not the same