Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H_{b} 89.36 77.83
point M_{a} 65 40

color 220 0 0
fontsize 11

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

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

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



% 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:  circles k(E_{c},C) and k(M_{a},B) intersect% DET:  circles k(E_{c},C) and k(M_{a},B) are not the same; points H_{b} and C must be different
% Constructing a line L_{\_G58715} which passes through point E_{c} and point M_{a}
line L_{\_G58715} E_{c} M_{a} 

color 200 200 200
drawline L_{\_G58715}
color 0 0 0


% Constructing a point C which is an image of the point H_{b} in the symmetry to point/line L_{\_G58715}
sim C L_{\_G58715} H_{b} 
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 B such that M_{a}B/M_{a}C=-1
towards B M_{a} C -1 
cmark_b B
color 200 200 200
drawsegment C B 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



% NDG:  line a and circle k(E_{c},C) intersect% DET:  points C and H_{a} must be different
% Constructing a point P_{\_G59132} which is a foot of the point E_{c} on the line a
foot P_{\_G59132} E_{c} a 
cmark_r P_{\_G59132}
color 200 200 200
drawline E_{c} P_{\_G59132} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point C in the symmetry to point/line P_{\_G59132}
sim H_{a} P_{\_G59132} C 
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 b and h_{a} are not parallel% DET:  lines b and h_{a} are not the same
% Constructing a point A which belongs to line b and line h_{a}
intersec A b h_{a} 
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

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