Construction in GCLC language

dim 120 120

point A 80 95
point C 110 40
point E_{c} 95 56.36

color 220 0 0
fontsize 11

cmark_t A
cmark_b C
cmark_r E_{c}
color 0 0 0
fontsize 10


% Constructing a point M_{b} such that AM_{b}/AC=0.5
towards M_{b} A C 0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment A C 
color 0 0 0



% 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


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

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



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

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



% NDG:  points 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 A
circle k(M_{b},C) M_{b} 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 A and H_{a} must be different
% Constructing a point P_{\_G6431} which is a foot of the point M_{b} on the line h_{a}
foot P_{\_G6431} M_{b} h_{a} 
cmark_r P_{\_G6431}
color 200 200 200
drawline M_{b} P_{\_G6431} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G6431}
sim H_{a} P_{\_G6431} A 
cmark_b H_{a}


% 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



% NDG:  line h_{c} and circle k(M_{b},C) intersect% DET:  points C and H_{c} must be different
% Constructing a point P_{\_G6669} which is a foot of the point M_{b} on the line h_{c}
foot P_{\_G6669} M_{b} h_{c} 
cmark_r P_{\_G6669}
color 200 200 200
drawline M_{b} P_{\_G6669} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G6669}
sim H_{c} P_{\_G6669} C 
cmark_lt H_{c}


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

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 A and M_{b} are not the same
% Determination conditions:  lines a and c are not the same; points H_{c} and A are not the same; points C and H_{c} must be different; points H_{a} and C are not the same; points A and H_{a} must be different; points C and E_{c} are not the same; points A and H are not the same