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 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 
% 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




% Generating number V[_G103951] with value 0.19259615318343046
number V[_G103951] 0.19259615318343046 


% Calculating value V[_G103972] using formula V[_G103951]*360
expression V[_G103972]  { V[_G103951]*360  } 


% Constructing a point H_{c} which is an image of the point V[_G103972] in a rotation around the point N for the angle M_{a}
rotate H_{c} N V[_G103972] M_{a} 
color 220 0 0
fontsize 11
cmark_lt H_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{a} V[_G103972] 
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} 
cmark_r E_{a}


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

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



% NDG:  circles k(N,M_{a}) and k(M_{a},B) intersect% DET:  circles k(N,M_{a}) and k(M_{a},B) are not the same; points H_{c} and H_{b} must be different
% Constructing a line L_{\_G104462} which passes through point N and point M_{a}
line L_{\_G104462} N M_{a} 

color 200 200 200
drawline L_{\_G104462}
color 0 0 0


% Constructing a point H_{b} which is an image of the point H_{c} in the symmetry to point/line L_{\_G104462}
sim H_{b} L_{\_G104462} H_{c} 
cmark_rt H_{b}



% Generating number V[_G104564] with value 0.19259615318343046
number V[_G104564] 0.19259615318343046 


% Calculating value V[_G104585] using formula V[_G104564]*360
expression V[_G104585]  { V[_G104564]*360  } 


% Constructing a point A which is an image of the point V[_G104585] in a rotation around the point E_{a} for the angle H_{c}
rotate A E_{a} V[_G104585] H_{c} 
cmark_t A
color 200 200 200
drawarc_p E_{a} H_{c} V[_G104585] 
color 0 0 0



% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
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_{b} and H are not the same
% Constructing a line h_{b} which passes through point H_{b} and point H
line h_{b} H_{b} H 

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



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



% Constructing a point C such that M_{a}C/M_{a}B=-1
towards C M_{a} B -1 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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