Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point E_{b} 50 56.36
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline h_{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 h_{b} and circle k(E_{a},A) intersect% DET:  points H_{b} and H must be different
% Constructing a point P_{\_G27228} which is a foot of the point E_{a} on the line h_{b}
foot P_{\_G27228} E_{a} h_{b} 
cmark_r P_{\_G27228}
color 200 200 200
drawline E_{a} P_{\_G27228} 
color 0 0 0

% Constructing a point H which is an image of the point H_{b} in the symmetry to point/line P_{\_G27228}
sim H P_{\_G27228} H_{b} 
cmark_rt H



% Constructing a point A such that HA/HE_{a}=2
towards A H E_{a} 2 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0



% Constructing a point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0


% 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



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

color 200 200 200
drawline c
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_{\_G27665} which is a foot of the point E_{a} on the line c
foot P_{\_G27665} E_{a} c 
cmark_r P_{\_G27665}
color 200 200 200
drawline E_{a} P_{\_G27665} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point A in the symmetry to point/line P_{\_G27665}
sim H_{c} P_{\_G27665} A 
cmark_lt H_{c}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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