Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_r N
color 0 0 0
fontsize 10


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

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



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

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



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




% Constructing a free point A
point A 80 95

cmark_t A



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  line b and circle k(N,M_{a}) intersect% DET:  points M_{b} and H_{b} must be different
% Constructing a point P_{\_G37398} which is a foot of the point N on the line b
foot P_{\_G37398} N b 
cmark_r P_{\_G37398}
color 200 200 200
drawline N P_{\_G37398} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point M_{b} in the symmetry to point/line P_{\_G37398}
sim H_{b} P_{\_G37398} M_{b} 
cmark_rt H_{b}


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

color 200 200 200
drawline h_{b}
color 0 0 0



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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



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


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



% Constructing a line L_{\_G37942} which passes through point N and point H
line L_{\_G37942} N H 

color 200 200 200
drawline L_{\_G37942}
color 0 0 0


% Constructing a point P_{\_G38043} with coordinates (0,0)
point P_{\_G38043} 0 0 
cmark_r P_{\_G38043}

% Constructing a point P_{\_G37967} such that NP_{\_G37967}/NP_{\_G38043}=-1
towards P_{\_G37967} N P_{\_G38043} -1 
cmark_r P_{\_G37967}
color 200 200 200
drawsegment P_{\_G38043} P_{\_G37967} 
color 0 0 0

% Constructing a point P_{\_G38012} such that NP_{\_G38012}/NP_{\_G38043}=3
towards P_{\_G38012} N P_{\_G38043} 3 
cmark_r P_{\_G38012}
color 200 200 200
drawsegment N P_{\_G38012} 
color 0 0 0

% Constructing a line L_{\_G37973} which passes through point H and point P_{\_G38012}
line L_{\_G37973} H P_{\_G38012} 

color 200 200 200
drawline L_{\_G37973}
color 0 0 0


% Constructing a line L_{\_G37936} which contains the point P_{\_G37967} and is parallel to the line L_{\_G37973}
parallel L_{\_G37936} P_{\_G37967} L_{\_G37973} 

color 200 200 200
drawline L_{\_G37936}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G37936} and line L_{\_G37942}
intersec G L_{\_G37936} L_{\_G37942} 
cmark_t G



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



drawsegment A B
drawsegment A C
drawsegment B C

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