Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H 80 72.73

color 220 0 0
fontsize 11

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


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

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

color 200 200 200
drawsegment H C 
color 0 0 0



% Constructing a free point A
point A 80 95

cmark_t A



% Constructing a point E_{a} such that AE_{a}/AH=0.5
towards E_{a} A H 0.5 
cmark_r E_{a}
color 200 200 200
drawsegment A H 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline h_{c}
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 b and circle k(E_{a},A) intersect% DET:  points A and H_{b} must be different
% Constructing a point P_{\_G25218} which is a foot of the point E_{a} on the line b
foot P_{\_G25218} E_{a} b 
cmark_r P_{\_G25218}
color 200 200 200
drawline E_{a} P_{\_G25218} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point A in the symmetry to point/line P_{\_G25218}
sim H_{b} P_{\_G25218} A 
cmark_rt H_{b}


% 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



% NDG:  line h_{c} and circle k(E_{a},A) intersect% DET:  points H and H_{c} must be different
% Constructing a point P_{\_G25456} which is a foot of the point E_{a} on the line h_{c}
foot P_{\_G25456} E_{a} h_{c} 
cmark_r P_{\_G25456}
color 200 200 200
drawline E_{a} P_{\_G25456} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G25456}
sim H_{c} P_{\_G25456} H 
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 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 A and E_{a} are not the same
% Determination conditions:  lines h_{b} and c are not the same; points H_{c} and A are not the same; points H and H_{c} must be different; points H_{b} and H are not the same; points A and H_{b} must be different; points E_{c} and H are not the same; points A and C are not the same