Construction in GCLC language

dim 120 120

point A 80 95
point E_{a} 80 83.86
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{a}
cmark_lt M_{c}
color 0 0 0
fontsize 10


% 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 AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


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

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

color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0



% NDG:  line c and circle k(E_{a},A) intersect% DET:  points A and H_{c} must be different
% Constructing a point P_{\_G14541} which is a foot of the point E_{a} on the line c
foot P_{\_G14541} E_{a} c 
cmark_r P_{\_G14541}
color 200 200 200
drawline E_{a} P_{\_G14541} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point A in the symmetry to point/line P_{\_G14541}
sim H_{c} P_{\_G14541} A 
cmark_lt H_{c}


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

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



% NDG:  line h_{b} and circle k(E_{a},A) intersect% DET:  points H and H_{b} must be different
% Constructing a point P_{\_G14779} which is a foot of the point E_{a} on the line h_{b}
foot P_{\_G14779} E_{a} h_{b} 
cmark_r P_{\_G14779}
color 200 200 200
drawline E_{a} P_{\_G14779} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point H in the symmetry to point/line P_{\_G14779}
sim H_{b} P_{\_G14779} H 
cmark_rt H_{b}


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

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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