Construction in GCLC language

dim 120 120

point M_{a} 65 40
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b M_{a}
cmark_r N
color 0 0 0
fontsize 10


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

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



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

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



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




% Constructing a free point A
point A 80 95

cmark_t A



% Constructing a line L_{\_G46780} which passes through point A and point M_{a}
line L_{\_G46780} A M_{a} 

color 200 200 200
drawline L_{\_G46780}
color 0 0 0


% Constructing a point P_{\_G46881} with coordinates (0,0)
point P_{\_G46881} 0 0 
cmark_r P_{\_G46881}

% Constructing a point P_{\_G46805} such that AP_{\_G46805}/AP_{\_G46881}=2
towards P_{\_G46805} A P_{\_G46881} 2 
cmark_r P_{\_G46805}
color 200 200 200
drawsegment A P_{\_G46805} 
color 0 0 0

% Constructing a point P_{\_G46850} such that AP_{\_G46850}/AP_{\_G46881}=3
towards P_{\_G46850} A P_{\_G46881} 3 
cmark_r P_{\_G46850}
color 200 200 200
drawsegment A P_{\_G46850} 
color 0 0 0

% Constructing a line L_{\_G46811} which passes through point M_{a} and point P_{\_G46850}
line L_{\_G46811} M_{a} P_{\_G46850} 

color 200 200 200
drawline L_{\_G46811}
color 0 0 0


% Constructing a line L_{\_G46774} which contains the point P_{\_G46805} and is parallel to the line L_{\_G46811}
parallel L_{\_G46774} P_{\_G46805} L_{\_G46811} 

color 200 200 200
drawline L_{\_G46774}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G46774} and line L_{\_G46780}
intersec G L_{\_G46774} L_{\_G46780} 
cmark_t G



% Constructing a point O such that NO/NG=3
towards O N G 3 
cmark_t O
color 200 200 200
drawsegment N O 
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:  line h_{a} and circle k(N,M_{a}) intersect% DET:  points E_{a} and H_{a} must be different
% Constructing a point P_{\_G47657} which is a foot of the point N on the line h_{a}
foot P_{\_G47657} N h_{a} 
cmark_r P_{\_G47657}
color 200 200 200
drawline N P_{\_G47657} 
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_{\_G47657}
sim H_{a} P_{\_G47657} 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:  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:  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; points A and O are not the same; line h_{a} and circle k(N,M_{a}) intersect; line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect; points M_{a} and N 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; points M_{a} and E_{a} must be different; points M_{a} and N are not the same