Construction in GCLC language

dim 120 120

point H 80 72.73
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H
cmark_r N
color 0 0 0
fontsize 10


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

% Constructing a point O such that HO/HN=2
towards O H N 2 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0



% Constructing a line L_{\_G56823} which passes through point H and point N
line L_{\_G56823} H N 

color 200 200 200
drawline L_{\_G56823}
color 0 0 0


% Constructing a point P_{\_G56924} with coordinates (0,0)
point P_{\_G56924} 0 0 
cmark_r P_{\_G56924}

% Constructing a point P_{\_G56848} such that HP_{\_G56848}/HP_{\_G56924}=4
towards P_{\_G56848} H P_{\_G56924} 4 
cmark_r P_{\_G56848}
color 200 200 200
drawsegment H P_{\_G56848} 
color 0 0 0

% Constructing a point P_{\_G56893} such that HP_{\_G56893}/HP_{\_G56924}=3
towards P_{\_G56893} H P_{\_G56924} 3 
cmark_r P_{\_G56893}
color 200 200 200
drawsegment H P_{\_G56893} 
color 0 0 0

% Constructing a line L_{\_G56854} which passes through point N and point P_{\_G56893}
line L_{\_G56854} N P_{\_G56893} 

color 200 200 200
drawline L_{\_G56854}
color 0 0 0


% Constructing a line L_{\_G56817} which contains the point P_{\_G56848} and is parallel to the line L_{\_G56854}
parallel L_{\_G56817} P_{\_G56848} L_{\_G56854} 

color 200 200 200
drawline L_{\_G56817}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G56817} and line L_{\_G56823}
intersec G L_{\_G56817} L_{\_G56823} 
color 220 0 0
fontsize 11
cmark_t G
color 0 0 0
fontsize 10




% Constructing a free point A
point A 80 95

cmark_t A



% 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



% 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


% 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 E_{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 E_{a}
circle k(N,M_{a}) N E_{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_{\_G57945} which is a foot of the point N on the line h_{a}
foot P_{\_G57945} N h_{a} 
cmark_r P_{\_G57945}
color 200 200 200
drawline N P_{\_G57945} 
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_{\_G57945}
sim H_{a} P_{\_G57945} 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 E_{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