Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H_{a} 80 40
point M_{c} 50 67.5

color 220 0 0
fontsize 11

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

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

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



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

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line h_{a} and circle k(M_{c},A) intersect% DET:  points H_{a} and A must be different
% Constructing a point P_{\_G29215} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G29215} M_{c} h_{a} 
cmark_r P_{\_G29215}
color 200 200 200
drawline M_{c} P_{\_G29215} 
color 0 0 0

% Constructing a point A which is an image of the point H_{a} in the symmetry to point/line P_{\_G29215}
sim A P_{\_G29215} H_{a} 
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 B such that M_{c}B/M_{c}A=-1
towards B M_{c} A -1 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


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

color 200 200 200
drawline a
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_{c},A) intersect% DET:  points B and H_{b} must be different
% Constructing a point P_{\_G29652} which is a foot of the point M_{c} on the line h_{b}
foot P_{\_G29652} M_{c} h_{b} 
cmark_r P_{\_G29652}
color 200 200 200
drawline M_{c} P_{\_G29652} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G29652}
sim H_{b} P_{\_G29652} B 
cmark_rt H_{b}


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

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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