Construction in GCLC language

dim 120 120

point A 80 95
point E_{a} 80 83.86
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{a}
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A 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_{\_G13021} which passes through point N and point H
line L_{\_G13021} N H 

color 200 200 200
drawline L_{\_G13021}
color 0 0 0


% Constructing a point P_{\_G13122} with coordinates (0,0)
point P_{\_G13122} 0 0 
cmark_r P_{\_G13122}

% Constructing a point P_{\_G13046} such that NP_{\_G13046}/NP_{\_G13122}=-1
towards P_{\_G13046} N P_{\_G13122} -1 
cmark_r P_{\_G13046}
color 200 200 200
drawsegment P_{\_G13122} P_{\_G13046} 
color 0 0 0

% Constructing a point P_{\_G13091} such that NP_{\_G13091}/NP_{\_G13122}=3
towards P_{\_G13091} N P_{\_G13122} 3 
cmark_r P_{\_G13091}
color 200 200 200
drawsegment N P_{\_G13091} 
color 0 0 0

% Constructing a line L_{\_G13052} which passes through point H and point P_{\_G13091}
line L_{\_G13052} H P_{\_G13091} 

color 200 200 200
drawline L_{\_G13052}
color 0 0 0


% Constructing a line L_{\_G13015} which contains the point P_{\_G13046} and is parallel to the line L_{\_G13052}
parallel L_{\_G13015} P_{\_G13046} L_{\_G13052} 

color 200 200 200
drawline L_{\_G13015}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G13015} and line L_{\_G13021}
intersec G L_{\_G13015} L_{\_G13021} 
cmark_t G



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

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_{\_G14017} which is a foot of the point N on the line h_{a}
foot P_{\_G14017} N h_{a} 
cmark_r P_{\_G14017}
color 200 200 200
drawline N P_{\_G14017} 
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_{\_G14017}
sim H_{a} P_{\_G14017} 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 E_{a} are not the same