Construction in GCLC language

dim 120 120

point B 20 40
point O 65 51.14
point G 70 58.33

color 220 0 0
fontsize 11

cmark_b B
cmark_t O
cmark_t G
color 0 0 0
fontsize 10


% Constructing a point M_{b} such that BM_{b}/BG=1.5
towards M_{b} B G 1.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b} 
color 0 0 0



% 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 B and H are not the same
% Constructing a line h_{b} which passes through point B and point H
line h_{b} B H 

color 200 200 200
drawline h_{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




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

color 200 200 200
drawline b
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
% Determination conditions:  points B and H are not the same