Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_lt M_{c}
cmark_r N
color 0 0 0
fontsize 10


% point E_{c} is given by the problem setting, but it has to be constructible this way, otherwise the problem has no solution
% DET:  points M_{c} and N are not the same
% Constructing a line m(H_{b}H_{a}) which passes through point M_{c} and point N
line m(H_{b}H_{a}) M_{c} N 

color 200 200 200
drawline m(H_{b}H_{a})
color 0 0 0



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

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



% NDG:  line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect% DET:  points M_{c} and E_{c} must be different
% Constructing a point E_{c} which is an image of the point M_{c} in the symmetry to point/line N
sim E_{c} N M_{c} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10




% Constructing a free point A
point A 80 95

cmark_t A



% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  line c and circle k(N,M_{a}) intersect% DET:  points M_{c} and H_{c} must be different
% Constructing a point P_{\_G58404} which is a foot of the point N on the line c
foot P_{\_G58404} N c 
cmark_r P_{\_G58404}
color 200 200 200
drawline N P_{\_G58404} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point M_{c} in the symmetry to point/line P_{\_G58404}
sim H_{c} P_{\_G58404} M_{c} 
cmark_lt H_{c}


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

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



% NDG:  points A and M_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point A
circle k(M_{c},A) M_{c} A 

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  circles k(N,M_{a}) and k(M_{c},A) intersect% DET:  circles k(N,M_{a}) and k(M_{c},A) are not the same
% Constructing points H_{a} and H_{b} which are in intersection of k(N,M_{a}) and k(M_{c},A)
intersec2 H_{a} H_{b} k(N,M_{a}) k(M_{c},A) 
cmark_b H_{a}
cmark_rt H_{b}


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

color 200 200 200
drawline h_{a}
color 0 0 0



% NDG:  lines h_{c} and h_{a} are not parallel% DET:  lines h_{c} and h_{a} are not the same
% Constructing a point H which belongs to line h_{c} and line h_{a}
intersec H h_{c} h_{a} 
cmark_rt H



% Constructing a line L_{\_G58948} which passes through point N and point H
line L_{\_G58948} N H 

color 200 200 200
drawline L_{\_G58948}
color 0 0 0


% Constructing a point P_{\_G59049} with coordinates (0,0)
point P_{\_G59049} 0 0 
cmark_r P_{\_G59049}

% Constructing a point P_{\_G58973} such that NP_{\_G58973}/NP_{\_G59049}=-1
towards P_{\_G58973} N P_{\_G59049} -1 
cmark_r P_{\_G58973}
color 200 200 200
drawsegment P_{\_G59049} P_{\_G58973} 
color 0 0 0

% Constructing a point P_{\_G59018} such that NP_{\_G59018}/NP_{\_G59049}=3
towards P_{\_G59018} N P_{\_G59049} 3 
cmark_r P_{\_G59018}
color 200 200 200
drawsegment N P_{\_G59018} 
color 0 0 0

% Constructing a line L_{\_G58979} which passes through point H and point P_{\_G59018}
line L_{\_G58979} H P_{\_G59018} 

color 200 200 200
drawline L_{\_G58979}
color 0 0 0


% Constructing a line L_{\_G58942} which contains the point P_{\_G58973} and is parallel to the line L_{\_G58979}
parallel L_{\_G58942} P_{\_G58973} L_{\_G58979} 

color 200 200 200
drawline L_{\_G58942}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G58942} and line L_{\_G58948}
intersec G L_{\_G58942} L_{\_G58948} 
cmark_t G



% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines h_{c} and h_{a} are not parallel; circles k(N,M_{a}) and k(M_{c},A) intersect; points A and M_{c} are not the same; line c and circle k(N,M_{a}) intersect; line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect; points M_{c} and N are not the same
% Determination conditions:  lines h_{c} and h_{a} are not the same; points A and H_{a} are not the same; circles k(N,M_{a}) and k(M_{c},A) are not the same; points H_{c} and E_{c} are not the same; points M_{c} and H_{c} must be different; points A and M_{c} are not the same; points M_{c} and E_{c} must be different; points M_{c} and N are not the same