Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_lt H_{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 H_{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 H_{c}
circle k(N,M_{a}) N H_{c} 

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




% Generating number V[_G55537] with value 0.2772784260842044
number V[_G55537] 0.2772784260842044 


% Calculating value V[_G55558] using formula V[_G55537]*360
expression V[_G55558]  { V[_G55537]*360  } 


% Constructing a point H_{b} which is an image of the point V[_G55558] in a rotation around the point N for the angle H_{c}
rotate H_{b} N V[_G55558] H_{c} 
color 220 0 0
fontsize 11
cmark_rt H_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{c} V[_G55558] 
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:  line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect
% Constructing points M_{a} and E_{a} which are in intersection of k(N,M_{a}) and m(H_{b}H_{c})
intersec2 M_{a} E_{a} k(N,M_{a}) m(H_{b}H_{c}) 
cmark_b M_{a}
cmark_r E_{a}



% Generating number V[_G55993] with value 0.2772784260842044
number V[_G55993] 0.2772784260842044 


% Calculating value V[_G56014] using formula V[_G55993]*360
expression V[_G56014]  { V[_G55993]*360  } 


% Constructing a point A which is an image of the point V[_G56014] in a rotation around the point E_{a} for the angle H_{b}
rotate A E_{a} V[_G56014] H_{b} 
cmark_t A
color 200 200 200
drawarc_p E_{a} H_{b} V[_G56014] 
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_{c} and N 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 H_{b} and H_{c} are not the same