Construction in GCLC language

dim 120 120

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

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_lt M_{c}
cmark_t O
color 0 0 0
fontsize 10

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

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



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

color 200 200 200
drawline m_{c}
color 0 0 0




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

color 200 200 200
drawline c
color 0 0 0



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

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

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


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



% Constructing a line L_{\_G42204} which passes through point N and point O
line L_{\_G42204} N O 

color 200 200 200
drawline L_{\_G42204}
color 0 0 0


% Constructing a point P_{\_G42305} with coordinates (0,0)
point P_{\_G42305} 0 0 
cmark_r P_{\_G42305}

% Constructing a point P_{\_G42229} such that NP_{\_G42229}/NP_{\_G42305}=1
towards P_{\_G42229} N P_{\_G42305} 1 
cmark_r P_{\_G42229}
color 200 200 200
drawsegment N P_{\_G42229} 
color 0 0 0

% Constructing a point P_{\_G42274} such that NP_{\_G42274}/NP_{\_G42305}=3
towards P_{\_G42274} N P_{\_G42305} 3 
cmark_r P_{\_G42274}
color 200 200 200
drawsegment N P_{\_G42274} 
color 0 0 0

% Constructing a line L_{\_G42235} which passes through point O and point P_{\_G42274}
line L_{\_G42235} O P_{\_G42274} 

color 200 200 200
drawline L_{\_G42235}
color 0 0 0


% Constructing a line L_{\_G42198} which contains the point P_{\_G42229} and is parallel to the line L_{\_G42235}
parallel L_{\_G42198} P_{\_G42229} L_{\_G42235} 

color 200 200 200
drawline L_{\_G42198}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G42198} and line L_{\_G42204}
intersec G L_{\_G42198} L_{\_G42204} 
cmark_t G



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


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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