Construction in GCLC language

dim 120 120

point A 80 95
point H_{a} 80 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_t A
cmark_b H_{a}
cmark_b I
color 0 0 0
fontsize 10

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

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




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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point I is not incident to the line a
% Constructing a point P_{\_G23262} which is a foot of the point I on the line a
foot P_{\_G23262} I a 
cmark_r P_{\_G23262}
color 200 200 200
drawline I P_{\_G23262} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G23262}
circle k(I,P_{a}) I P_{\_G23262} 

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_{\_G23496} of the segment AI
midpoint P_{\_G23496} A I 
cmark_r P_{\_G23496}

% Constructing a circle C_{\_G23499} whose center is at point P_{\_G23496} and which passes through point A
circle C_{\_G23499} P_{\_G23496} A 

color 200 200 200
drawcircle C_{\_G23499}
color 0 0 0


% Constructing points P_{\_G23502} and P_{\_G23505} which are in intersection of C_{\_G23499} and k(I,P_{a})
intersec2 P_{\_G23502} P_{\_G23505} C_{\_G23499} k(I,P_{a}) 
cmark_r P_{\_G23502}
cmark_r P_{\_G23505}

% Constructing a line c which passes through point A and point P_{\_G23502}
line c A P_{\_G23502} 

color 200 200 200
drawline c
color 0 0 0


% Constructing a line b which passes through point A and point P_{\_G23505}
line b A P_{\_G23505} 

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
% Determination conditions:  lines a and b are not the same; lines c and a are not the same; points A and H_{a} are not the same