Construction in GCLC language

dim 120 120

point H_{a} 80 40
point T_{a} 70.86 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_b T_{a}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawline s_{a}
color 0 0 0




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

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



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


% NDG:  point I is not incident to the line a
% Constructing a point P_{\_G59007} which is a foot of the point I on the line a
foot P_{\_G59007} I a 
cmark_r P_{\_G59007}
color 200 200 200
drawline I P_{\_G59007} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G59007}
circle k(I,P_{a}) I P_{\_G59007} 

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



% NDG:  point A is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G59241} of the segment AI
midpoint P_{\_G59241} A I 
cmark_r P_{\_G59241}

% Constructing a circle C_{\_G59244} whose center is at point P_{\_G59241} and which passes through point A
circle C_{\_G59244} P_{\_G59241} A 

color 200 200 200
drawcircle C_{\_G59244}
color 0 0 0


% Constructing points P_{\_G59247} and P_{\_G59250} which are in intersection of C_{\_G59244} and k(I,P_{a})
intersec2 P_{\_G59247} P_{\_G59250} C_{\_G59244} k(I,P_{a}) 
cmark_r P_{\_G59247}
cmark_r P_{\_G59250}

% Constructing a line c which passes through point A and point P_{\_G59247}
line c A P_{\_G59247} 

color 200 200 200
drawline c
color 0 0 0


% Constructing a line b which passes through point A and point P_{\_G59250}
line b A P_{\_G59250} 

color 200 200 200
drawline b
color 0 0 0



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


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



drawsegment A B
drawsegment A C
drawsegment B C

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