Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

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


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

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0




% Generating number V[_G43832] with value 0.3266611733732241
number V[_G43832] 0.3266611733732241 


% Calculating value V[_G43853] using formula V[_G43832]*360
expression V[_G43853]  { V[_G43832]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G43853] in a rotation around the point E_{b} for the angle H_{c}
rotate H_{a} E_{b} V[_G43853] H_{c} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p E_{b} H_{c} V[_G43853] 
color 0 0 0


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

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

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


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

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

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


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


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

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



% NDG:  line m(H_{a}H_{c}) and circle k(N,M_{a}) intersect% DET:  points E_{b} and M_{b} must be different
% Constructing a point M_{b} which is an image of the point E_{b} in the symmetry to point/line N
sim M_{b} N E_{b} 
cmark_rt M_{b}



% Generating number V[_G44618] with value 0.3266611733732241
number V[_G44618] 0.3266611733732241 


% Calculating value V[_G44639] using formula V[_G44618]*360
expression V[_G44639]  { V[_G44618]*360  } 


% Constructing a point A which is an image of the point V[_G44639] in a rotation around the point M_{b} for the angle H_{a}
rotate A M_{b} V[_G44639] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{b} H_{a} V[_G44639] 
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 point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H 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; line m(H_{a}H_{c}) and circle k(N,M_{a}) intersect; points H_{a} and N are not the same; lines m(H_{a}H_{c}) and m(H_{a}E_{b}) are not parallel; points H_{c} and E_{b} 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; points E_{b} and M_{b} must be different; lines m(H_{a}H_{c}) and m(H_{a}E_{b}) are not the same; points H_{a} and H_{c} are not the same; points H_{a} and E_{b} are not the same