Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H_{b} 89.36 77.83
point M_{b} 95 67.5

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_rt H_{b}
cmark_rt M_{b}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline b
color 0 0 0



% NDG:  points H_{b} 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 H_{b}
circle k(E_{a},A) E_{a} H_{b} 

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



% NDG:  line b and circle k(E_{a},A) intersect% DET:  points H_{b} and A must be different
% Constructing a point P_{\_G43690} which is a foot of the point E_{a} on the line b
foot P_{\_G43690} E_{a} b 
cmark_r P_{\_G43690}
color 200 200 200
drawline E_{a} P_{\_G43690} 
color 0 0 0

% Constructing a point A which is an image of the point H_{b} in the symmetry to point/line P_{\_G43690}
sim A P_{\_G43690} H_{b} 
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_{b} and H are not the same
% Constructing a line h_{b} which passes through point H_{b} and point H
line h_{b} H_{b} H 

color 200 200 200
drawline h_{b}
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(E_{a},A) intersect% DET:  points H and H_{c} must be different
% Constructing a point P_{\_G44127} which is a foot of the point E_{a} on the line h_{c}
foot P_{\_G44127} E_{a} h_{c} 
cmark_r P_{\_G44127}
color 200 200 200
drawline E_{a} P_{\_G44127} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G44127}
sim H_{c} P_{\_G44127} H 
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 h_{b} and c are not parallel% DET:  lines h_{b} and c are not the same
% Constructing a point B which belongs to line h_{b} and line c
intersec B h_{b} c 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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