Construction in GCLC language

dim 120 120

point H_{a} 80 40
point N 72.5 61.93
point O 65 51.14

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_r N
cmark_t O
color 0 0 0
fontsize 10


% Constructing a line L_{\_G80147} which passes through point N and point O
line L_{\_G80147} N O 

color 200 200 200
drawline L_{\_G80147}
color 0 0 0


% Constructing a point P_{\_G80248} with coordinates (0,0)
point P_{\_G80248} 0 0 
cmark_r P_{\_G80248}

% Constructing a point P_{\_G80172} such that NP_{\_G80172}/NP_{\_G80248}=1
towards P_{\_G80172} N P_{\_G80248} 1 
cmark_r P_{\_G80172}
color 200 200 200
drawsegment N P_{\_G80172} 
color 0 0 0

% Constructing a point P_{\_G80217} such that NP_{\_G80217}/NP_{\_G80248}=3
towards P_{\_G80217} N P_{\_G80248} 3 
cmark_r P_{\_G80217}
color 200 200 200
drawsegment N P_{\_G80217} 
color 0 0 0

% Constructing a line L_{\_G80178} which passes through point O and point P_{\_G80217}
line L_{\_G80178} O P_{\_G80217} 

color 200 200 200
drawline L_{\_G80178}
color 0 0 0


% Constructing a line L_{\_G80141} which contains the point P_{\_G80172} and is parallel to the line L_{\_G80178}
parallel L_{\_G80141} P_{\_G80172} L_{\_G80178} 

color 200 200 200
drawline L_{\_G80141}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G80141} and line L_{\_G80147}
intersec G L_{\_G80141} L_{\_G80147} 
cmark_t G



% Constructing a point H such that NH/NO=-1
towards H N O -1 
cmark_rt H
color 200 200 200
drawsegment O H 
color 0 0 0


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

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



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

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line h_{a} and circle k(N,M_{a}) intersect% DET:  points H_{a} and E_{a} must be different
% Constructing a point P_{\_G81075} which is a foot of the point N on the line h_{a}
foot P_{\_G81075} N h_{a} 
cmark_r P_{\_G81075}
color 200 200 200
drawline N P_{\_G81075} 
color 0 0 0

% Constructing a point E_{a} which is an image of the point H_{a} in the symmetry to point/line P_{\_G81075}
sim E_{a} P_{\_G81075} H_{a} 
cmark_r E_{a}



% 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



% Constructing a point M_{a} such that GM_{a}/GA=-0.5
towards M_{a} G A -0.5 
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a} 
color 0 0 0


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

color 200 200 200
drawline 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 a and circle k(O,C) intersect
% Constructing points C and B which are in intersection of k(O,C) and a
intersec2 C B k(O,C) a 
cmark_b C
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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