Construction in GCLC language

dim 120 120

point H 80 72.73
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_rt H
cmark_rt H_{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 and H_{b} are not the same
% Constructing a line h_{b} which passes through point H and point H_{b}
line h_{b} H H_{b} 

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




% Constructing a point E_{b} such that HE_{b}/HH_{b}=0.3002171731662424
towards E_{b} H H_{b} 0.3002171731662424 
color 220 0 0
fontsize 11
cmark_r E_{b}
color 0 0 0
fontsize 10

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



% 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


% NDG:  points H 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
circle k(E_{b},B) E_{b} H 

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




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

color 200 200 200
drawline b
color 0 0 0




% Constructing a point P_{\_G62777} with coordinates (10,30)
point P_{\_G62777} 10 30 
cmark_r P_{\_G62777}

% Constructing a line L_{\_G62780} which passes through point E_{b} and point H_{b}
line L_{\_G62780} E_{b} H_{b} 

color 200 200 200
drawline L_{\_G62780}
color 0 0 0


% Constructing a line L_{\_G62783} which is perpendicular to line L_{\_G62780} and which passes through point H_{b}
perp L_{\_G62783} H_{b} L_{\_G62780} 

color 200 200 200
drawline L_{\_G62783}
color 0 0 0


% Constructing a line L_{\_G62786} which passes through point E_{b} and point P_{\_G62777}
line L_{\_G62786} E_{b} P_{\_G62777} 

color 200 200 200
drawline L_{\_G62786}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G62786} and line L_{\_G62783}
intersec A L_{\_G62786} L_{\_G62783} 
cmark_t A


% DET:  points A and H are not the same
% Constructing a line h_{a} which passes through point A and point H
line h_{a} A H 

color 200 200 200
drawline h_{a}
color 0 0 0



% NDG:  line h_{a} and circle k(E_{b},B) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G63187} which is a foot of the point E_{b} on the line h_{a}
foot P_{\_G63187} E_{b} h_{a} 
cmark_r P_{\_G63187}
color 200 200 200
drawline E_{b} P_{\_G63187} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G63187}
sim H_{a} P_{\_G63187} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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