Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_lt H_{c}
color 0 0 0
fontsize 10


% point H_{b} is given by the problem setting, but it has to belong to the circle k(E_{a},A) which is constructible from the others objects given 
% NDG:  points H_{c} and E_{a} are not the same
% Constructing a circle k(E_{a},A) whose center is at point E_{a} and which passes through point H_{c}
circle k(E_{a},A) E_{a} H_{c} 

color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0




% Generating number V[_G62185] with value 0.6151650272760504
number V[_G62185] 0.6151650272760504 


% Calculating value V[_G62206] using formula V[_G62185]*360
expression V[_G62206]  { V[_G62185]*360  } 


% Constructing a point H_{b} which is an image of the point V[_G62206] in a rotation around the point E_{a} for the angle H_{c}
rotate H_{b} E_{a} V[_G62206] H_{c} 
color 220 0 0
fontsize 11
cmark_rt H_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p E_{a} H_{c} V[_G62206] 
color 0 0 0


% DET:  points H_{b} and E_{a} are not the same
% Constructing bisector m(H_{b}E_{a}) of the segment H_{b}E_{a}
med m(H_{b}E_{a}) H_{b} E_{a} 

color 200 200 200
drawline m(H_{b}E_{a})
color 0 0 0

color 200 200 200
drawsegment H_{b} E_{a} 
color 0 0 0


% DET:  points H_{b} and H_{c} are not the same
% Constructing bisector m(H_{b}H_{c}) of the segment H_{b}H_{c}
med m(H_{b}H_{c}) H_{b} H_{c} 

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

color 200 200 200
drawsegment H_{b} H_{c} 
color 0 0 0


% NDG:  lines m(H_{b}H_{c}) and m(H_{b}E_{a}) are not parallel% DET:  lines m(H_{b}H_{c}) and m(H_{b}E_{a}) are not the same
% Constructing a point N which belongs to line m(H_{b}H_{c}) and line m(H_{b}E_{a})
intersec N m(H_{b}H_{c}) m(H_{b}E_{a}) 
cmark_r N


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

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 E_{a} and M_{a} must be different
% Constructing a point M_{a} which is an image of the point E_{a} in the symmetry to point/line N
sim M_{a} N E_{a} 
cmark_b M_{a}



% Generating number V[_G62971] with value 0.6151650272760504
number V[_G62971] 0.6151650272760504 


% Calculating value V[_G62992] using formula V[_G62971]*360
expression V[_G62992]  { V[_G62971]*360  } 


% Constructing a point A which is an image of the point V[_G62992] in a rotation around the point E_{a} for the angle H_{b}
rotate A E_{a} V[_G62992] H_{b} 
cmark_t A
color 200 200 200
drawarc_p E_{a} H_{b} V[_G62992] 
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_{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_{c} and H are not the same
% Constructing a line h_{c} which passes through point H_{c} and point H
line h_{c} H_{c} H 

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



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



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



drawsegment A B
drawsegment A C
drawsegment B C

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