Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point T_{b} 94.25 68.88
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_rt T_{b}
cmark_b I
color 0 0 0
fontsize 10

% 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



% DET:  points T_{b} and I are not the same
% Constructing a line s_{b} which passes through point T_{b} and point I
line s_{b} T_{b} I 

color 200 200 200
drawline s_{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



% NDG:  lines h_{b} and s_{b} are not parallel% DET:  lines h_{b} and s_{b} are not the same
% Constructing a point B which belongs to line h_{b} and line s_{b}
intersec B h_{b} s_{b} 
cmark_b B


% NDG:  point I is not incident to the line b
% Constructing a point P_{\_G58685} which is a foot of the point I on the line b
foot P_{\_G58685} I b 
cmark_r P_{\_G58685}
color 200 200 200
drawline I P_{\_G58685} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G58685}
circle k(I,P_{a}) I P_{\_G58685} 

color 200 200 200
drawcircle k(I,P_{a})
color 0 0 0



% NDG:  point B is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G58919} of the segment BI
midpoint P_{\_G58919} B I 
cmark_r P_{\_G58919}

% Constructing a circle C_{\_G58922} whose center is at point P_{\_G58919} and which passes through point B
circle C_{\_G58922} P_{\_G58919} B 

color 200 200 200
drawcircle C_{\_G58922}
color 0 0 0


% Constructing points P_{\_G58925} and P_{\_G58928} which are in intersection of C_{\_G58922} and k(I,P_{a})
intersec2 P_{\_G58925} P_{\_G58928} C_{\_G58922} k(I,P_{a}) 
cmark_r P_{\_G58925}
cmark_r P_{\_G58928}

% Constructing a line c which passes through point B and point P_{\_G58925}
line c B P_{\_G58925} 

color 200 200 200
drawline c
color 0 0 0


% Constructing a line a which passes through point B and point P_{\_G58928}
line a B P_{\_G58928} 

color 200 200 200
drawline a
color 0 0 0



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


% 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; lines c and b are not parallel; point B is outside the circle k(I,P_{a}); point I is not incident to the line b; lines h_{b} and s_{b} are not parallel
% Determination conditions:  lines b and a are not the same; lines c and b are not the same; lines h_{b} and s_{b} are not the same; points T_{b} and I are not the same; points H_{b} and T_{b} are not the same