Construction in GCLC language

dim 120 120

point C 110 40
point E_{c} 95 56.36
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b C
cmark_r E_{c}
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point H such that CH/CE_{c}=2
towards H C E_{c} 2 
cmark_rt H
color 200 200 200
drawsegment C H 
color 0 0 0



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



% Constructing a line L_{\_G23965} which passes through point N and point H
line L_{\_G23965} N H 

color 200 200 200
drawline L_{\_G23965}
color 0 0 0


% Constructing a point P_{\_G24066} with coordinates (0,0)
point P_{\_G24066} 0 0 
cmark_r P_{\_G24066}

% Constructing a point P_{\_G23990} such that NP_{\_G23990}/NP_{\_G24066}=-1
towards P_{\_G23990} N P_{\_G24066} -1 
cmark_r P_{\_G23990}
color 200 200 200
drawsegment P_{\_G24066} P_{\_G23990} 
color 0 0 0

% Constructing a point P_{\_G24035} such that NP_{\_G24035}/NP_{\_G24066}=3
towards P_{\_G24035} N P_{\_G24066} 3 
cmark_r P_{\_G24035}
color 200 200 200
drawsegment N P_{\_G24035} 
color 0 0 0

% Constructing a line L_{\_G23996} which passes through point H and point P_{\_G24035}
line L_{\_G23996} H P_{\_G24035} 

color 200 200 200
drawline L_{\_G23996}
color 0 0 0


% Constructing a line L_{\_G23959} which contains the point P_{\_G23990} and is parallel to the line L_{\_G23996}
parallel L_{\_G23959} P_{\_G23990} L_{\_G23996} 

color 200 200 200
drawline L_{\_G23959}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G23959} and line L_{\_G23965}
intersec G L_{\_G23959} L_{\_G23965} 
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 C and E_{c} are not the same
% Constructing a line h_{c} which passes through point C and point E_{c}
line h_{c} C E_{c} 

color 200 200 200
drawline h_{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:  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_{\_G24961} which is a foot of the point N on the line h_{c}
foot P_{\_G24961} N h_{c} 
cmark_r P_{\_G24961}
color 200 200 200
drawline N P_{\_G24961} 
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_{\_G24961}
sim H_{c} P_{\_G24961} 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:  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; line h_{c} and circle k(N,M_{a}) intersect; points E_{c} and N are not the same; points C and O 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 C and E_{c} are not the same