Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point T_{c} 55.38 72.43
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_lt H_{c}
cmark_lt T_{c}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline s_{c}
color 0 0 0




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

color 200 200 200
drawline h_{c}
color 0 0 0



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


% NDG:  point I is not incident to the line c
% Constructing a point P_{\_G66018} which is a foot of the point I on the line c
foot P_{\_G66018} I c 
cmark_r P_{\_G66018}
color 200 200 200
drawline I P_{\_G66018} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G66018}
circle k(I,P_{a}) I P_{\_G66018} 

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



% NDG:  point C is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G66252} of the segment CI
midpoint P_{\_G66252} C I 
cmark_r P_{\_G66252}

% Constructing a circle C_{\_G66255} whose center is at point P_{\_G66252} and which passes through point C
circle C_{\_G66255} P_{\_G66252} C 

color 200 200 200
drawcircle C_{\_G66255}
color 0 0 0


% Constructing points P_{\_G66258} and P_{\_G66261} which are in intersection of C_{\_G66255} and k(I,P_{a})
intersec2 P_{\_G66258} P_{\_G66261} C_{\_G66255} k(I,P_{a}) 
cmark_r P_{\_G66258}
cmark_r P_{\_G66261}

% Constructing a line a which passes through point C and point P_{\_G66258}
line a C P_{\_G66258} 

color 200 200 200
drawline a
color 0 0 0


% Constructing a line b which passes through point C and point P_{\_G66261}
line b C P_{\_G66261} 

color 200 200 200
drawline b
color 0 0 0



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


% 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



drawsegment A B
drawsegment A C
drawsegment B C

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