Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H 80 72.73

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_rt H
color 0 0 0
fontsize 10


% point A is given by the problem setting, but it has to be constructible this way, otherwise the problem has no solution

% Constructing a point A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1 
color 220 0 0
fontsize 11
cmark_t A
color 0 0 0
fontsize 10

color 200 200 200
drawsegment H A 
color 0 0 0



% Constructing a free point B
point B 20 40

cmark_b B



% Constructing a point E_{b} such that BE_{b}/BH=0.5
towards E_{b} B H 0.5 
cmark_r E_{b}
color 200 200 200
drawsegment B H 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



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

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



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

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0



% NDG:  line c and circle k(E_{b},B) intersect% DET:  points B and H_{c} must be different
% Constructing a point P_{\_G11504} which is a foot of the point E_{b} on the line c
foot P_{\_G11504} E_{b} c 
cmark_r P_{\_G11504}
color 200 200 200
drawline E_{b} P_{\_G11504} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point B in the symmetry to point/line P_{\_G11504}
sim H_{c} P_{\_G11504} B 
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_{a} and circle k(E_{b},B) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G11742} which is a foot of the point E_{b} on the line h_{a}
foot P_{\_G11742} E_{b} h_{a} 
cmark_r P_{\_G11742}
color 200 200 200
drawline E_{b} P_{\_G11742} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G11742}
sim H_{a} P_{\_G11742} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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