Construction in GCLC language

dim 120 120

point C 110 40
point E_{a} 80 83.86
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

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

% DET:  points C and H_{b} are not the same
% Constructing a line b which passes through point C and point H_{b}
line b C H_{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_{\_G16514} which is a foot of the point E_{a} on the line b
foot P_{\_G16514} E_{a} b 
cmark_r P_{\_G16514}
color 200 200 200
drawline E_{a} P_{\_G16514} 
color 0 0 0

% Constructing a point A which is an image of the point H_{b} in the symmetry to point/line P_{\_G16514}
sim A P_{\_G16514} H_{b} 
cmark_t A



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


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

color 200 200 200
drawline h_{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



% NDG:  line h_{c} and circle k(E_{a},A) intersect% DET:  points H and H_{c} must be different
% Constructing a point P_{\_G16877} which is a foot of the point E_{a} on the line h_{c}
foot P_{\_G16877} E_{a} h_{c} 
cmark_r P_{\_G16877}
color 200 200 200
drawline E_{a} P_{\_G16877} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G16877}
sim H_{c} P_{\_G16877} 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_{b} and H are not the same; points C and H are not the same; points H_{b} and A must be different; points C and H_{b} are not the same