Construction in GCLC language

dim 120 120

point B 20 40
point H_{a} 80 40
point I 74.37 61.15

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline 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:  point I is not incident to the line a
% Constructing a point P_{\_G23387} which is a foot of the point I on the line a
foot P_{\_G23387} I a 
cmark_r P_{\_G23387}
color 200 200 200
drawline I P_{\_G23387} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G23387}
circle k(I,P_{a}) I P_{\_G23387} 

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 a point P_{\_G23594} which is a foot of the point I on the line a
foot P_{\_G23594} I a 
cmark_r P_{\_G23594}
color 200 200 200
drawline I P_{\_G23594} 
color 0 0 0

% Constructing a line L_{\_G23597} which passes through point I and point B
line L_{\_G23597} I B 

color 200 200 200
drawline L_{\_G23597}
color 0 0 0


% Constructing a point P_{\_G23600} which is an image of the point P_{\_G23594} in the symmetry to point/line L_{\_G23597}
sim P_{\_G23600} L_{\_G23597} P_{\_G23594} 
cmark_r P_{\_G23600}

% Constructing a line c which passes through point B and point P_{\_G23600}
line c B P_{\_G23600} 

color 200 200 200
drawline c
color 0 0 0



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


% NDG:  point A is outside the circle k(I,P_{a})
% Constructing a point P_{\_G23986} which is a foot of the point I on the line c
foot P_{\_G23986} I c 
cmark_r P_{\_G23986}
color 200 200 200
drawline I P_{\_G23986} 
color 0 0 0

% Constructing a line L_{\_G23989} which passes through point I and point A
line L_{\_G23989} I A 

color 200 200 200
drawline L_{\_G23989}
color 0 0 0


% Constructing a point P_{\_G23992} which is an image of the point P_{\_G23986} in the symmetry to point/line L_{\_G23989}
sim P_{\_G23992} L_{\_G23989} P_{\_G23986} 
cmark_r P_{\_G23992}

% Constructing a line b which passes through point A and point P_{\_G23992}
line b A P_{\_G23992} 

color 200 200 200
drawline b
color 0 0 0



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