Construction in GCLC language

dim 120 120

point B 20 40
point E_{a} 80 83.86
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b B
cmark_r E_{a}
cmark_r N
color 0 0 0
fontsize 10

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

color 200 200 200
drawline m(H_{b}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_{b}H_{c}) and circle k(N,M_{a}) intersect% DET:  points E_{a} and M_{a} must be different
% Constructing a point M_{a} which is an image of the point E_{a} in the symmetry to point/line N
sim M_{a} N E_{a} 
cmark_b M_{a}



% 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


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

color 200 200 200
drawline a
color 0 0 0



% NDG:  line a and circle k(N,M_{a}) intersect% DET:  points M_{a} and H_{a} must be different
% Constructing a point P_{\_G16636} which is a foot of the point N on the line a
foot P_{\_G16636} N a 
cmark_r P_{\_G16636}
color 200 200 200
drawline N P_{\_G16636} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point M_{a} in the symmetry to point/line P_{\_G16636}
sim H_{a} P_{\_G16636} M_{a} 
cmark_b H_{a}


% DET:  points H_{a} and E_{a} are not the same
% Constructing a line h_{a} which passes through point H_{a} and point E_{a}
line h_{a} H_{a} E_{a} 

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



% NDG:  points 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 B
circle k(M_{a},B) M_{a} B 

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



% NDG:  circles k(N,M_{a}) and k(M_{a},B) intersect% DET:  circles k(N,M_{a}) and k(M_{a},B) are not the same
% Constructing points H_{b} and H_{c} which are in intersection of k(N,M_{a}) and k(M_{a},B)
intersec2 H_{b} H_{c} k(N,M_{a}) k(M_{a},B) 
cmark_rt H_{b}
cmark_lt H_{c}


% DET:  points B and H_{b} are not the same
% Constructing a line h_{b} which passes through point B and point H_{b}
line h_{b} B H_{b} 

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



% NDG:  lines h_{a} and h_{b} are not parallel% DET:  lines h_{a} and h_{b} are not the same
% Constructing a point H which belongs to line h_{a} and line h_{b}
intersec H h_{a} h_{b} 
cmark_rt H



% Constructing a point A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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