Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point M_{b} 95 67.5

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_rt M_{b}
color 0 0 0
fontsize 10


% point E_{b} is given by the problem setting, but it has to belong to the line h_{b} which is constructible from the others objects given 
% DET:  points H_{b} and M_{b} are not the same
% Constructing a line b which passes through point H_{b} and point M_{b}
line b H_{b} M_{b} 

color 200 200 200
drawline b
color 0 0 0




% Constructing a line h_{b} which is perpendicular to line b and which passes through point H_{b}
perp h_{b} H_{b} b 

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




% Constructing a point P_{\_G40760} with coordinates (10,30)
point P_{\_G40760} 10 30 
cmark_r P_{\_G40760}

% Constructing a line L_{\_G40763} which passes through point M_{b} and point H_{b}
line L_{\_G40763} M_{b} H_{b} 

color 200 200 200
drawline L_{\_G40763}
color 0 0 0


% Constructing a line L_{\_G40766} which is perpendicular to line L_{\_G40763} and which passes through point H_{b}
perp L_{\_G40766} H_{b} L_{\_G40763} 

color 200 200 200
drawline L_{\_G40766}
color 0 0 0


% Constructing a line L_{\_G40769} which passes through point M_{b} and point P_{\_G40760}
line L_{\_G40769} M_{b} P_{\_G40760} 

color 200 200 200
drawline L_{\_G40769}
color 0 0 0


% Constructing a point E_{b} which belongs to line L_{\_G40769} and line L_{\_G40766}
intersec E_{b} L_{\_G40769} L_{\_G40766} 
color 220 0 0
fontsize 11
cmark_r E_{b}
color 0 0 0
fontsize 10



% DET:  points E_{b} and M_{b} are not the same
% Constructing a line m(H_{a}H_{c}) which passes through point E_{b} and point M_{b}
line m(H_{a}H_{c}) E_{b} M_{b} 

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



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

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

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


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


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

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




% Constructing a point A such that H_{b}A/H_{b}M_{b}=0.06639255160865681
towards A H_{b} M_{b} 0.06639255160865681 
cmark_t A
color 200 200 200
drawsegment H_{b} M_{b} 
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


% NDG:  points 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 A
circle k(M_{b},C) M_{b} 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
% Constructing points H_{a} and H_{c} which are in intersection of k(N,M_{a}) and k(M_{b},C)
intersec2 H_{a} H_{c} k(N,M_{a}) k(M_{b},C) 
cmark_b H_{a}
cmark_lt H_{c}


% 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



% NDG:  lines h_{b} and h_{a} are not parallel% DET:  lines h_{b} and h_{a} are not the same
% Constructing a point H which belongs to line h_{b} and line h_{a}
intersec H h_{b} h_{a} 
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_{b} and h_{a} are not parallel; circles k(N,M_{a}) and k(M_{b},C) intersect; points A and M_{b} are not the same; points E_{b} and N are not the same; lines m(E_{b}H_{b}) and m(H_{a}H_{c}) are not parallel
% Determination conditions:  lines h_{b} and h_{a} 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; lines m(E_{b}H_{b}) and m(H_{a}H_{c}) are not the same; points E_{b} and H_{b} are not the same; points E_{b} and M_{b} are not the same; points H_{b} and M_{b} are not the same