Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_rt T_{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 T_{b} are not the same
% Constructing a line b which passes through point H_{b} and point T_{b}
line b H_{b} T_{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_{\_G54548} with coordinates (10,30)
point P_{\_G54548} 10 30 
cmark_r P_{\_G54548}

% Constructing a line L_{\_G54551} which passes through point T_{b} and point H_{b}
line L_{\_G54551} T_{b} H_{b} 

color 200 200 200
drawline L_{\_G54551}
color 0 0 0


% Constructing a line L_{\_G54554} which is perpendicular to line L_{\_G54551} and which passes through point H_{b}
perp L_{\_G54554} H_{b} L_{\_G54551} 

color 200 200 200
drawline L_{\_G54554}
color 0 0 0


% Constructing a line L_{\_G54557} which passes through point T_{b} and point P_{\_G54548}
line L_{\_G54557} T_{b} P_{\_G54548} 

color 200 200 200
drawline L_{\_G54557}
color 0 0 0


% Constructing a point E_{b} which belongs to line L_{\_G54557} and line L_{\_G54554}
intersec E_{b} L_{\_G54557} L_{\_G54554} 
color 220 0 0
fontsize 11
cmark_r E_{b}
color 0 0 0
fontsize 10




% Constructing a point A such that H_{b}A/H_{b}T_{b}=0.2750948355167641
towards A H_{b} T_{b} 0.2750948355167641 
cmark_t A
color 200 200 200
drawsegment H_{b} T_{b} 
color 0 0 0



% Constructing a point B such that E_{b}B/E_{b}H_{b}=0.2750948355167641
towards B E_{b} H_{b} 0.2750948355167641 
cmark_b B
color 200 200 200
drawsegment E_{b} H_{b} 
color 0 0 0



% Constructing a point H such that BH/BE_{b}=2
towards H B E_{b} 2 
cmark_rt H
color 200 200 200
drawsegment B H 
color 0 0 0


% DET:  points B and A are not the same
% Constructing a line c which passes through point B and point A
line c B A 

color 200 200 200
drawline c
color 0 0 0



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

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



% NDG:  line c and circle k(E_{b},B) intersect% DET:  points B and H_{c} must be different
% Constructing a point P_{\_G55313} which is a foot of the point E_{b} on the line c
foot P_{\_G55313} E_{b} c 
cmark_r P_{\_G55313}
color 200 200 200
drawline E_{b} P_{\_G55313} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point B in the symmetry to point/line P_{\_G55313}
sim H_{c} P_{\_G55313} B 
cmark_lt H_{c}


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

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



drawsegment A B
drawsegment A C
drawsegment B C

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