Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point E_{c} 95 56.36
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_r E_{c}
cmark_b M_{a}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline m(CH_{b})
color 0 0 0



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

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

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


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

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

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


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


% NDG:  points E_{b} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{b}
circle k(N,M_{a}) N E_{b} 

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0




% Constructing a line h_{b} which contains the point E_{b} and is parallel to the line m(CH_{b})
parallel h_{b} E_{b} m(CH_{b}) 

color 200 200 200
drawline h_{b}
color 0 0 0



% NDG:  line h_{b} and circle k(N,M_{a}) intersect% DET:  points E_{b} and H_{b} must be different
% Constructing a point P_{\_G63240} which is a foot of the point N on the line h_{b}
foot P_{\_G63240} N h_{b} 
cmark_r P_{\_G63240}
color 200 200 200
drawline N P_{\_G63240} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point E_{b} in the symmetry to point/line P_{\_G63240}
sim H_{b} P_{\_G63240} E_{b} 
cmark_rt H_{b}


% NDG:  points H_{b} and E_{c} are not the same
% Constructing a circle k(E_{c},C) whose center is at point E_{c} and which passes through point H_{b}
circle k(E_{c},C) E_{c} H_{b} 

color 200 200 200
drawcircle k(E_{c},C)
color 0 0 0



% NDG:  line h_{b} and circle k(E_{c},C) intersect% DET:  points H_{b} and H must be different
% Constructing a point P_{\_G63544} which is a foot of the point E_{c} on the line h_{b}
foot P_{\_G63544} E_{c} h_{b} 
cmark_r P_{\_G63544}
color 200 200 200
drawline E_{c} P_{\_G63544} 
color 0 0 0

% Constructing a point H which is an image of the point H_{b} in the symmetry to point/line P_{\_G63544}
sim H P_{\_G63544} H_{b} 
cmark_rt H



% Constructing a point B such that HB/HE_{b}=2
towards B H E_{b} 2 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0



% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1 
cmark_b C
color 200 200 200
drawsegment H C 
color 0 0 0



% Constructing a line L_{\_G63806} which passes through point N and point H
line L_{\_G63806} N H 

color 200 200 200
drawline L_{\_G63806}
color 0 0 0


% Constructing a point P_{\_G63907} with coordinates (0,0)
point P_{\_G63907} 0 0 
cmark_r P_{\_G63907}

% Constructing a point P_{\_G63831} such that NP_{\_G63831}/NP_{\_G63907}=-1
towards P_{\_G63831} N P_{\_G63907} -1 
cmark_r P_{\_G63831}
color 200 200 200
drawsegment P_{\_G63907} P_{\_G63831} 
color 0 0 0

% Constructing a point P_{\_G63876} such that NP_{\_G63876}/NP_{\_G63907}=3
towards P_{\_G63876} N P_{\_G63907} 3 
cmark_r P_{\_G63876}
color 200 200 200
drawsegment N P_{\_G63876} 
color 0 0 0

% Constructing a line L_{\_G63837} which passes through point H and point P_{\_G63876}
line L_{\_G63837} H P_{\_G63876} 

color 200 200 200
drawline L_{\_G63837}
color 0 0 0


% Constructing a line L_{\_G63800} which contains the point P_{\_G63831} and is parallel to the line L_{\_G63837}
parallel L_{\_G63800} P_{\_G63831} L_{\_G63837} 

color 200 200 200
drawline L_{\_G63800}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G63800} and line L_{\_G63806}
intersec G L_{\_G63800} L_{\_G63806} 
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



drawsegment A B
drawsegment A C
drawsegment B C

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