Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H 80 72.73
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_rt H
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1 
cmark_b C
color 200 200 200
drawsegment H C 
color 0 0 0



% 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_{\_G60717} which passes through point H and point N
line L_{\_G60717} H N 

color 200 200 200
drawline L_{\_G60717}
color 0 0 0


% Constructing a point P_{\_G60818} with coordinates (0,0)
point P_{\_G60818} 0 0 
cmark_r P_{\_G60818}

% Constructing a point P_{\_G60742} such that HP_{\_G60742}/HP_{\_G60818}=4
towards P_{\_G60742} H P_{\_G60818} 4 
cmark_r P_{\_G60742}
color 200 200 200
drawsegment H P_{\_G60742} 
color 0 0 0

% Constructing a point P_{\_G60787} such that HP_{\_G60787}/HP_{\_G60818}=3
towards P_{\_G60787} H P_{\_G60818} 3 
cmark_r P_{\_G60787}
color 200 200 200
drawsegment H P_{\_G60787} 
color 0 0 0

% Constructing a line L_{\_G60748} which passes through point N and point P_{\_G60787}
line L_{\_G60748} N P_{\_G60787} 

color 200 200 200
drawline L_{\_G60748}
color 0 0 0


% Constructing a line L_{\_G60711} which contains the point P_{\_G60742} and is parallel to the line L_{\_G60748}
parallel L_{\_G60711} P_{\_G60742} L_{\_G60748} 

color 200 200 200
drawline L_{\_G60711}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G60711} and line L_{\_G60717}
intersec G L_{\_G60711} L_{\_G60717} 
cmark_t G



% Constructing a point M_{c} such that CM_{c}/CG=1.5
towards M_{c} C G 1.5 
cmark_lt M_{c}
color 200 200 200
drawsegment C M_{c} 
color 0 0 0


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

color 200 200 200
drawline h_{c}
color 0 0 0



% NDG:  points E_{c} 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_{c}
circle k(N,M_{a}) N E_{c} 

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



% NDG:  line h_{c} and circle k(N,M_{a}) intersect% DET:  points E_{c} and H_{c} must be different
% Constructing a point P_{\_G61654} which is a foot of the point N on the line h_{c}
foot P_{\_G61654} N h_{c} 
cmark_r P_{\_G61654}
color 200 200 200
drawline N P_{\_G61654} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point E_{c} in the symmetry to point/line P_{\_G61654}
sim H_{c} P_{\_G61654} E_{c} 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



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

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



% NDG:  line c and circle k(O,C) intersect
% Constructing points A and B which are in intersection of k(O,C) and c
intersec2 A B k(O,C) c 
cmark_t A
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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