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 H_{b} 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_{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




% Generating number V[_G88407] with value 0.12005895510745553
number V[_G88407] 0.12005895510745553 


% Calculating value V[_G88428] using formula V[_G88407]*360
expression V[_G88428]  { V[_G88407]*360  } 


% Constructing a point H_{b} which is an image of the point V[_G88428] in a rotation around the point N for the angle M_{c}
rotate H_{b} N V[_G88428] M_{c} 
color 220 0 0
fontsize 11
cmark_rt H_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{c} V[_G88428] 
color 0 0 0


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

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; points H_{b} and H_{a} must be different
% Constructing a line L_{\_G88842} which passes through point N and point M_{c}
line L_{\_G88842} N M_{c} 

color 200 200 200
drawline L_{\_G88842}
color 0 0 0


% Constructing a point H_{a} which is an image of the point H_{b} in the symmetry to point/line L_{\_G88842}
sim H_{a} L_{\_G88842} H_{b} 
cmark_b H_{a}



% Generating number V[_G88944] with value 0.12005895510745553
number V[_G88944] 0.12005895510745553 


% Calculating value V[_G88965] using formula V[_G88944]*360
expression V[_G88965]  { V[_G88944]*360  } 


% Constructing a point A which is an image of the point V[_G88965] in a rotation around the point M_{c} for the angle H_{b}
rotate A M_{c} V[_G88965] H_{b} 
cmark_t A
color 200 200 200
drawarc_p M_{c} H_{b} V[_G88965] 
color 0 0 0



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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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