Construction in GCLC language

dim 120 120

point A 80 95
point O 65 51.14
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_t A
cmark_t O
cmark_b I
color 0 0 0
fontsize 10

% DET:  points A and I are not the same
% Constructing a line s_{a} which passes through point A and point I
line s_{a} A I 

color 200 200 200
drawline s_{a}
color 0 0 0



% NDG:  points A and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point A
circle k(O,C) O A 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line s_{a} and circle k(O,C) intersect% DET:  points A and N_{a} must be different
% Constructing a point P_{\_G12122} which is a foot of the point O on the line s_{a}
foot P_{\_G12122} O s_{a} 
cmark_r P_{\_G12122}
color 200 200 200
drawline O P_{\_G12122} 
color 0 0 0

% Constructing a point N_{a} which is an image of the point A in the symmetry to point/line P_{\_G12122}
sim N_{a} P_{\_G12122} A 
cmark_b N_{a}


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

color 200 200 200
drawcircle k(N_{a},C)
color 0 0 0



% NDG:  circles k(O,C) and k(N_{a},C) intersect% DET:  circles k(O,C) and k(N_{a},C) are not the same
% Constructing points C and B which are in intersection of k(O,C) and k(N_{a},C)
intersec2 C B k(O,C) k(N_{a},C) 
cmark_b C
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  circles k(O,C) and k(N_{a},C) intersect; points I and N_{a} are not the same; line s_{a} and circle k(O,C) intersect; points A and O are not the same
% Determination conditions:  circles k(O,C) and k(N_{a},C) are not the same; points A and N_{a} must be different; points A and I are not the same