Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H_{a} 80 40
point M_{b} 95 67.5

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawcircle k(E_{c},C)
color 0 0 0



% 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:  circles k(E_{c},C) and k(M_{b},C) intersect% DET:  circles k(E_{c},C) and k(M_{b},C) are not the same; points H_{a} and C must be different
% Constructing a line L_{\_G59281} which passes through point E_{c} and point M_{b}
line L_{\_G59281} E_{c} M_{b} 

color 200 200 200
drawline L_{\_G59281}
color 0 0 0


% Constructing a point C which is an image of the point H_{a} in the symmetry to point/line L_{\_G59281}
sim C L_{\_G59281} H_{a} 
cmark_b C



% Constructing a point H such that CH/CE_{c}=2
towards H C E_{c} 2 
cmark_rt H
color 200 200 200
drawsegment C H 
color 0 0 0



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


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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawline b
color 0 0 0



% NDG:  line b and circle k(E_{c},C) intersect% DET:  points C and H_{b} must be different
% Constructing a point P_{\_G59698} which is a foot of the point E_{c} on the line b
foot P_{\_G59698} E_{c} b 
cmark_r P_{\_G59698}
color 200 200 200
drawline E_{c} P_{\_G59698} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point C in the symmetry to point/line P_{\_G59698}
sim H_{b} P_{\_G59698} C 
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 a and h_{b} are not parallel% DET:  lines a and h_{b} are not the same
% Constructing a point B which belongs to line a and line h_{b}
intersec B a h_{b} 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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