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 H_{c} is given by the problem setting, but it has to belong to the circle k(N,M_{a}) which is constructible from the others objects given 
% 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




% Generating number V[_G59157] with value 0.6502436698850995
number V[_G59157] 0.6502436698850995 


% Calculating value V[_G59178] using formula V[_G59157]*360
expression V[_G59178]  { V[_G59157]*360  } 


% Constructing a point H_{c} which is an image of the point V[_G59178] in a rotation around the point N for the angle M_{b}
rotate H_{c} N V[_G59178] M_{b} 
color 220 0 0
fontsize 11
cmark_lt H_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{b} V[_G59178] 
color 0 0 0


% NDG:  points H_{c} 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 H_{c}
circle k(M_{b},C) M_{b} H_{c} 

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; points H_{c} and H_{a} must be different
% Constructing a line L_{\_G59592} which passes through point N and point M_{b}
line L_{\_G59592} N M_{b} 

color 200 200 200
drawline L_{\_G59592}
color 0 0 0


% Constructing a point H_{a} which is an image of the point H_{c} in the symmetry to point/line L_{\_G59592}
sim H_{a} L_{\_G59592} H_{c} 
cmark_b H_{a}



% Generating number V[_G59694] with value 0.6502436698850995
number V[_G59694] 0.6502436698850995 


% Calculating value V[_G59715] using formula V[_G59694]*360
expression V[_G59715]  { V[_G59694]*360  } 


% Constructing a point A which is an image of the point V[_G59715] in a rotation around the point M_{b} for the angle H_{c}
rotate A M_{b} V[_G59715] H_{c} 
cmark_t A
color 200 200 200
drawarc_p M_{b} H_{c} V[_G59715] 
color 0 0 0



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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



% NDG:  lines c and a are not parallel% DET:  lines c and a are not the same
% Constructing a point B which belongs to line c and line a
intersec B c a 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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