Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H_{c} 68.91 84.83
point M_{b} 95 67.5

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0



% NDG:  points H_{c} 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_{c}
circle k(M_{b},C) M_{b} H_{c} 

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



% NDG:  circles k(E_{a},A) and k(M_{b},C) intersect% DET:  circles k(E_{a},A) and k(M_{b},C) are not the same; points H_{c} and A must be different
% Constructing a line L_{\_G46157} which passes through point E_{a} and point M_{b}
line L_{\_G46157} E_{a} M_{b} 

color 200 200 200
drawline L_{\_G46157}
color 0 0 0


% Constructing a point A which is an image of the point H_{c} in the symmetry to point/line L_{\_G46157}
sim A L_{\_G46157} H_{c} 
cmark_t A



% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0



% 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


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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline b
color 0 0 0



% NDG:  line b and circle k(E_{a},A) intersect% DET:  points A and H_{b} must be different
% Constructing a point P_{\_G46574} which is a foot of the point E_{a} on the line b
foot P_{\_G46574} E_{a} b 
cmark_r P_{\_G46574}
color 200 200 200
drawline E_{a} P_{\_G46574} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point A in the symmetry to point/line P_{\_G46574}
sim H_{b} P_{\_G46574} A 
cmark_rt H_{b}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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