Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H_{a} 80 40
point M_{b} 95 67.5

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b H_{a}
cmark_rt M_{b}
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_{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:  line h_{a} and circle k(M_{b},C) intersect% DET:  points H_{a} and A must be different
% Constructing a point P_{\_G42823} which is a foot of the point M_{b} on the line h_{a}
foot P_{\_G42823} M_{b} h_{a} 
cmark_r P_{\_G42823}
color 200 200 200
drawline M_{b} P_{\_G42823} 
color 0 0 0

% Constructing a point A which is an image of the point H_{a} in the symmetry to point/line P_{\_G42823}
sim A P_{\_G42823} 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 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_{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 H and C are not the same
% Constructing a line h_{c} which passes through point H and point C
line h_{c} H C 

color 200 200 200
drawline h_{c}
color 0 0 0



% NDG:  line h_{c} and circle k(M_{b},C) intersect% DET:  points C and H_{c} must be different
% Constructing a point P_{\_G43260} which is a foot of the point M_{b} on the line h_{c}
foot P_{\_G43260} M_{b} h_{c} 
cmark_r P_{\_G43260}
color 200 200 200
drawline M_{b} P_{\_G43260} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G43260}
sim H_{c} P_{\_G43260} C 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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