Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H_{c} 68.91 84.83
point M_{a} 65 40

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline h_{c}
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:  line h_{c} and circle k(M_{a},B) intersect% DET:  points H_{c} and C must be different
% Constructing a point P_{\_G56736} which is a foot of the point M_{a} on the line h_{c}
foot P_{\_G56736} M_{a} h_{c} 
cmark_r P_{\_G56736}
color 200 200 200
drawline M_{a} P_{\_G56736} 
color 0 0 0

% Constructing a point C which is an image of the point H_{c} in the symmetry to point/line P_{\_G56736}
sim C P_{\_G56736} H_{c} 
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_{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 H and B are not the same
% Constructing a line h_{b} which passes through point H and point B
line h_{b} H B 

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



% NDG:  line h_{b} and circle k(M_{a},B) intersect% DET:  points B and H_{b} must be different
% Constructing a point P_{\_G57173} which is a foot of the point M_{a} on the line h_{b}
foot P_{\_G57173} M_{a} h_{b} 
cmark_r P_{\_G57173}
color 200 200 200
drawline M_{a} P_{\_G57173} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G57173}
sim H_{b} P_{\_G57173} B 
cmark_rt H_{b}


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

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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