Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point E_{b} 50 56.36
point E_{c} 95 56.36

color 220 0 0
fontsize 11

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

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

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

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


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

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

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


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


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

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



% NDG:  points E_{a} 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_{a}
circle k(N,M_{a}) N E_{a} 

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



% NDG:  line m(H_{a}H_{c}) and circle k(N,M_{a}) intersect% DET:  points E_{b} and M_{b} must be different
% Constructing a point M_{b} which is an image of the point E_{b} in the symmetry to point/line N
sim M_{b} N E_{b} 
cmark_rt M_{b}


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

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




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

color 200 200 200
drawline h_{a}
color 0 0 0



% NDG:  line h_{a} and circle k(N,M_{a}) intersect% DET:  points E_{a} and H_{a} must be different
% Constructing a point P_{\_G20426} which is a foot of the point N on the line h_{a}
foot P_{\_G20426} N h_{a} 
cmark_r P_{\_G20426}
color 200 200 200
drawline N P_{\_G20426} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point E_{a} in the symmetry to point/line P_{\_G20426}
sim H_{a} P_{\_G20426} E_{a} 
cmark_b H_{a}


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

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0



% NDG:  line h_{a} and circle k(E_{b},B) intersect% DET:  points H_{a} and H must be different
% Constructing a point P_{\_G20730} which is a foot of the point E_{b} on the line h_{a}
foot P_{\_G20730} E_{b} h_{a} 
cmark_r P_{\_G20730}
color 200 200 200
drawline E_{b} P_{\_G20730} 
color 0 0 0

% Constructing a point H which is an image of the point H_{a} in the symmetry to point/line P_{\_G20730}
sim H P_{\_G20730} H_{a} 
cmark_rt H



% Constructing a point A such that HA/HE_{a}=2
towards A H E_{a} 2 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0



% Constructing a point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
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



drawsegment A B
drawsegment A C
drawsegment B C

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