Construction in GCLC language

dim 120 120

point C 110 40
point E_{a} 80 83.86
point E_{c} 95 56.36

color 220 0 0
fontsize 11

cmark_b C
cmark_r E_{a}
cmark_r E_{c}
color 0 0 0
fontsize 10


% Constructing a point H such that CH/CE_{c}=2
towards H C E_{c} 2 
cmark_rt H
color 200 200 200
drawsegment C H 
color 0 0 0



% Constructing a point A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0


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

color 200 200 200
drawline b
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 C and E_{c} are not the same
% Constructing a circle k(E_{c},C) whose center is at point E_{c} and which passes through point C
circle k(E_{c},C) E_{c} C 

color 200 200 200
drawcircle k(E_{c},C)
color 0 0 0



% NDG:  line b and circle k(E_{c},C) intersect% DET:  points C and H_{b} must be different
% Constructing a point P_{\_G23592} which is a foot of the point E_{c} on the line b
foot P_{\_G23592} E_{c} b 
cmark_r P_{\_G23592}
color 200 200 200
drawline E_{c} P_{\_G23592} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point C in the symmetry to point/line P_{\_G23592}
sim H_{b} P_{\_G23592} C 
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_{a} and circle k(E_{c},C) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G23830} which is a foot of the point E_{c} on the line h_{a}
foot P_{\_G23830} E_{c} h_{a} 
cmark_r P_{\_G23830}
color 200 200 200
drawline E_{c} P_{\_G23830} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G23830}
sim H_{a} P_{\_G23830} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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