Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H_{c} 68.91 84.83
point M_{a} 65 40

color 220 0 0
fontsize 11

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

% NDG:  points H_{c} 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_{c}
circle k(E_{b},B) E_{b} H_{c} 

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



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

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



% NDG:  circles k(E_{b},B) and k(M_{a},B) intersect% DET:  circles k(E_{b},B) and k(M_{a},B) are not the same; points H_{c} and B must be different
% Constructing a line L_{\_G60774} which passes through point E_{b} and point M_{a}
line L_{\_G60774} E_{b} M_{a} 

color 200 200 200
drawline L_{\_G60774}
color 0 0 0


% Constructing a point B which is an image of the point H_{c} in the symmetry to point/line L_{\_G60774}
sim B L_{\_G60774} H_{c} 
cmark_b B



% Constructing a point H such that BH/BE_{b}=2
towards H B E_{b} 2 
cmark_rt H
color 200 200 200
drawsegment B H 
color 0 0 0



% 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 H_{c} and B are not the same
% Constructing a line c which passes through point H_{c} and point B
line c H_{c} B 

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



% NDG:  line a and circle k(E_{b},B) intersect% DET:  points B and H_{a} must be different
% Constructing a point P_{\_G61191} which is a foot of the point E_{b} on the line a
foot P_{\_G61191} E_{b} a 
cmark_r P_{\_G61191}
color 200 200 200
drawline E_{b} P_{\_G61191} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point B in the symmetry to point/line P_{\_G61191}
sim H_{a} P_{\_G61191} B 
cmark_b H_{a}


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

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



% NDG:  lines c and h_{a} are not parallel% DET:  lines c and h_{a} are not the same
% Constructing a point A which belongs to line c and line h_{a}
intersec A c h_{a} 
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

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