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_{a} 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[_G78999] with value 0.7878809171087368
number V[_G78999] 0.7878809171087368 


% Calculating value V[_G79020] using formula V[_G78999]*360
expression V[_G79020]  { V[_G78999]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G79020] in a rotation around the point N for the angle M_{b}
rotate H_{a} N V[_G79020] M_{b} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{b} V[_G79020] 
color 0 0 0


% NDG:  points H_{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 H_{a}
circle k(M_{b},C) M_{b} H_{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; points H_{a} and H_{c} must be different
% Constructing a line L_{\_G79434} which passes through point N and point M_{b}
line L_{\_G79434} N M_{b} 

color 200 200 200
drawline L_{\_G79434}
color 0 0 0


% Constructing a point H_{c} which is an image of the point H_{a} in the symmetry to point/line L_{\_G79434}
sim H_{c} L_{\_G79434} H_{a} 
cmark_lt H_{c}



% Generating number V[_G79536] with value 0.7878809171087368
number V[_G79536] 0.7878809171087368 


% Calculating value V[_G79557] using formula V[_G79536]*360
expression V[_G79557]  { V[_G79536]*360  } 


% Constructing a point A which is an image of the point V[_G79557] in a rotation around the point M_{b} for the angle H_{a}
rotate A M_{b} V[_G79557] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{b} H_{a} V[_G79557] 
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_{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



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

color 200 200 200
drawline h_{c}
color 0 0 0



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



% Constructing a line L_{\_G79968} which passes through point N and point H
line L_{\_G79968} N H 

color 200 200 200
drawline L_{\_G79968}
color 0 0 0


% Constructing a point P_{\_G80069} with coordinates (0,0)
point P_{\_G80069} 0 0 
cmark_r P_{\_G80069}

% Constructing a point P_{\_G79993} such that NP_{\_G79993}/NP_{\_G80069}=-1
towards P_{\_G79993} N P_{\_G80069} -1 
cmark_r P_{\_G79993}
color 200 200 200
drawsegment P_{\_G80069} P_{\_G79993} 
color 0 0 0

% Constructing a point P_{\_G80038} such that NP_{\_G80038}/NP_{\_G80069}=3
towards P_{\_G80038} N P_{\_G80069} 3 
cmark_r P_{\_G80038}
color 200 200 200
drawsegment N P_{\_G80038} 
color 0 0 0

% Constructing a line L_{\_G79999} which passes through point H and point P_{\_G80038}
line L_{\_G79999} H P_{\_G80038} 

color 200 200 200
drawline L_{\_G79999}
color 0 0 0


% Constructing a line L_{\_G79962} which contains the point P_{\_G79993} and is parallel to the line L_{\_G79999}
parallel L_{\_G79962} P_{\_G79993} L_{\_G79999} 

color 200 200 200
drawline L_{\_G79962}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G79962} and line L_{\_G79968}
intersec G L_{\_G79962} L_{\_G79968} 
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_{a} and h_{c} are not parallel; circles k(N,M_{a}) and k(M_{b},C) intersect; points H_{a} and M_{b} are not the same; points M_{b} and N are not the same
% Determination conditions:  lines h_{a} and h_{c} are not the same; points H_{c} and C 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_{a} and H_{c} must be different