Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point M_{b} 95 67.5
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_rt M_{b}
cmark_t O
color 0 0 0
fontsize 10

% DET:  points E_{b} and M_{b} are not the same
% Constructing a line m(H_{a}H_{c}) which passes through point E_{b} and point M_{b}
line m(H_{a}H_{c}) E_{b} M_{b} 

color 200 200 200
drawline m(H_{a}H_{c})
color 0 0 0



% DET:  points M_{b} and O are not the same
% Constructing a line m_{b} which passes through point M_{b} and point O
line m_{b} M_{b} O 

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




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

color 200 200 200
drawline b
color 0 0 0



% DET:  points E_{b} and M_{b} are not the same
% Constructing bisector m(E_{b}M_{b}) of the segment E_{b}M_{b}
med m(E_{b}M_{b}) E_{b} M_{b} 

color 200 200 200
drawline m(E_{b}M_{b})
color 0 0 0

color 200 200 200
drawsegment E_{b} M_{b} 
color 0 0 0


% NDG:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not parallel% DET:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{b}M_{b}) and line m(H_{a}H_{c})
intersec N m(E_{b}M_{b}) m(H_{a}H_{c}) 
cmark_r N



% Constructing a line L_{\_G40800} which passes through point N and point O
line L_{\_G40800} N O 

color 200 200 200
drawline L_{\_G40800}
color 0 0 0


% Constructing a point P_{\_G40901} with coordinates (0,0)
point P_{\_G40901} 0 0 
cmark_r P_{\_G40901}

% Constructing a point P_{\_G40825} such that NP_{\_G40825}/NP_{\_G40901}=1
towards P_{\_G40825} N P_{\_G40901} 1 
cmark_r P_{\_G40825}
color 200 200 200
drawsegment N P_{\_G40825} 
color 0 0 0

% Constructing a point P_{\_G40870} such that NP_{\_G40870}/NP_{\_G40901}=3
towards P_{\_G40870} N P_{\_G40901} 3 
cmark_r P_{\_G40870}
color 200 200 200
drawsegment N P_{\_G40870} 
color 0 0 0

% Constructing a line L_{\_G40831} which passes through point O and point P_{\_G40870}
line L_{\_G40831} O P_{\_G40870} 

color 200 200 200
drawline L_{\_G40831}
color 0 0 0


% Constructing a line L_{\_G40794} which contains the point P_{\_G40825} and is parallel to the line L_{\_G40831}
parallel L_{\_G40794} P_{\_G40825} L_{\_G40831} 

color 200 200 200
drawline L_{\_G40794}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G40794} and line L_{\_G40800}
intersec G L_{\_G40794} L_{\_G40800} 
cmark_t G



% 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(E_{b}M_{b}) and m(H_{a}H_{c}) are not parallel
% Determination conditions:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not the same; points E_{b} and M_{b} are not the same; points M_{b} and O are not the same; points E_{b} and M_{b} are not the same