Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point M_{a} 65 40
point M_{c} 50 67.5

color 220 0 0
fontsize 11

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

% 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


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

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

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


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


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

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



% 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



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


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

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




% Constructing a line h_{b} which contains the point E_{b} and is parallel to the line m(AH_{b})
parallel h_{b} E_{b} m(AH_{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_{\_G62850} which is a foot of the point N on the line h_{b}
foot P_{\_G62850} N h_{b} 
cmark_r P_{\_G62850}
color 200 200 200
drawline N P_{\_G62850} 
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_{\_G62850}
sim H_{b} P_{\_G62850} E_{b} 
cmark_rt H_{b}


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

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



% NDG:  line h_{b} and circle k(M_{a},B) intersect% DET:  points H_{b} and B must be different
% Constructing a point P_{\_G63154} which is a foot of the point M_{a} on the line h_{b}
foot P_{\_G63154} M_{a} h_{b} 
cmark_r P_{\_G63154}
color 200 200 200
drawline M_{a} P_{\_G63154} 
color 0 0 0

% Constructing a point B which is an image of the point H_{b} in the symmetry to point/line P_{\_G63154}
sim B P_{\_G63154} H_{b} 
cmark_b B



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



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



drawsegment A B
drawsegment A C
drawsegment B C

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