Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point M_{b} 95 67.5
point M_{c} 50 67.5

color 220 0 0
fontsize 11

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

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

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

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


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

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

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


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


% DET:  points M_{b} and N are not the same
% Constructing a line m(H_{a}H_{c}) which passes through point M_{b} and point N
line m(H_{a}H_{c}) M_{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 M_{b} and E_{b} must be different
% Constructing a point E_{b} which is an image of the point M_{b} in the symmetry to point/line N
sim E_{b} N M_{b} 
cmark_r E_{b}


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

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




% Constructing a line h_{a} which contains the point E_{a} and is parallel to the line m(BH_{a})
parallel h_{a} E_{a} m(BH_{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_{\_G56440} which is a foot of the point N on the line h_{a}
foot P_{\_G56440} N h_{a} 
cmark_r P_{\_G56440}
color 200 200 200
drawline N P_{\_G56440} 
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_{\_G56440}
sim H_{a} P_{\_G56440} E_{a} 
cmark_b H_{a}


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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



% NDG:  line h_{a} and circle k(M_{b},C) intersect% DET:  points H_{a} and A must be different
% Constructing a point P_{\_G56744} which is a foot of the point M_{b} on the line h_{a}
foot P_{\_G56744} M_{b} h_{a} 
cmark_r P_{\_G56744}
color 200 200 200
drawline M_{b} P_{\_G56744} 
color 0 0 0

% Constructing a point A which is an image of the point H_{a} in the symmetry to point/line P_{\_G56744}
sim A P_{\_G56744} H_{a} 
cmark_t A



% Constructing a point C such that M_{b}C/M_{b}A=-1
towards C M_{b} A -1 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0



% Constructing a point B such that M_{c}B/M_{c}A=-1
towards B M_{c} A -1 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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