Construction in GCLC language

dim 120 120

point N 72.5 61.93
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r N
cmark_t O
color 0 0 0
fontsize 10


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

% Constructing a line L_{\_G63862} which passes through point N and point O
line L_{\_G63862} N O 

color 200 200 200
drawline L_{\_G63862}
color 0 0 0


% Constructing a point P_{\_G63963} with coordinates (0,0)
point P_{\_G63963} 0 0 
cmark_r P_{\_G63963}

% Constructing a point P_{\_G63887} such that NP_{\_G63887}/NP_{\_G63963}=1
towards P_{\_G63887} N P_{\_G63963} 1 
cmark_r P_{\_G63887}
color 200 200 200
drawsegment N P_{\_G63887} 
color 0 0 0

% Constructing a point P_{\_G63932} such that NP_{\_G63932}/NP_{\_G63963}=3
towards P_{\_G63932} N P_{\_G63963} 3 
cmark_r P_{\_G63932}
color 200 200 200
drawsegment N P_{\_G63932} 
color 0 0 0

% Constructing a line L_{\_G63893} which passes through point O and point P_{\_G63932}
line L_{\_G63893} O P_{\_G63932} 

color 200 200 200
drawline L_{\_G63893}
color 0 0 0


% Constructing a line L_{\_G63856} which contains the point P_{\_G63887} and is parallel to the line L_{\_G63893}
parallel L_{\_G63856} P_{\_G63887} L_{\_G63893} 

color 200 200 200
drawline L_{\_G63856}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G63856} and line L_{\_G63862}
intersec G L_{\_G63856} L_{\_G63862} 
cmark_t G



% Constructing a point H such that NH/NO=-1
towards H N O -1 
color 220 0 0
fontsize 11
cmark_rt H
color 0 0 0
fontsize 10

color 200 200 200
drawsegment O H 
color 0 0 0



% Constructing a free point A
point A 80 95

cmark_t A



% Constructing a point M_{a} such that AM_{a}/AG=1.5
towards M_{a} A G 1.5 
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a} 
color 0 0 0



% 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 H are not the same
% Constructing a line h_{a} which passes through point A and point H
line h_{a} A H 

color 200 200 200
drawline h_{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:  points M_{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 M_{a}
circle k(N,M_{a}) N M_{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 E_{a} and H_{a} must be different
% Constructing a point P_{\_G41458} which is a foot of the point N on the line h_{a}
foot P_{\_G41458} N h_{a} 
cmark_r P_{\_G41458}
color 200 200 200
drawline N P_{\_G41458} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point E_{a} in the symmetry to point/line P_{\_G41458}
sim H_{a} P_{\_G41458} E_{a} 
cmark_b H_{a}


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