Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point M_{a} 65 40
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b M_{a}
cmark_t O
color 0 0 0
fontsize 10

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

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



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

color 200 200 200
drawline m_{a}
color 0 0 0




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

color 200 200 200
drawline a
color 0 0 0



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

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

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


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



% Constructing a line L_{\_G40240} which passes through point N and point O
line L_{\_G40240} N O 

color 200 200 200
drawline L_{\_G40240}
color 0 0 0


% Constructing a point P_{\_G40341} with coordinates (0,0)
point P_{\_G40341} 0 0 
cmark_r P_{\_G40341}

% Constructing a point P_{\_G40265} such that NP_{\_G40265}/NP_{\_G40341}=1
towards P_{\_G40265} N P_{\_G40341} 1 
cmark_r P_{\_G40265}
color 200 200 200
drawsegment N P_{\_G40265} 
color 0 0 0

% Constructing a point P_{\_G40310} such that NP_{\_G40310}/NP_{\_G40341}=3
towards P_{\_G40310} N P_{\_G40341} 3 
cmark_r P_{\_G40310}
color 200 200 200
drawsegment N P_{\_G40310} 
color 0 0 0

% Constructing a line L_{\_G40271} which passes through point O and point P_{\_G40310}
line L_{\_G40271} O P_{\_G40310} 

color 200 200 200
drawline L_{\_G40271}
color 0 0 0


% Constructing a line L_{\_G40234} which contains the point P_{\_G40265} and is parallel to the line L_{\_G40271}
parallel L_{\_G40234} P_{\_G40265} L_{\_G40271} 

color 200 200 200
drawline L_{\_G40234}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G40234} and line L_{\_G40240}
intersec G L_{\_G40234} L_{\_G40240} 
cmark_t G



% Constructing a point A such that M_{a}A/M_{a}G=3
towards A M_{a} G 3 
cmark_t A
color 200 200 200
drawsegment M_{a} A 
color 0 0 0


% NDG:  points A and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point A
circle k(O,C) O A 

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



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line a and circle k(O,C) intersect; points A and O are not the same; lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not parallel
% Determination conditions:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not the same; points E_{a} and M_{a} are not the same; points M_{a} and O are not the same; points E_{a} and M_{a} are not the same