Construction in GCLC language

dim 120 120

point A 80 95
point H_{c} 68.91 84.83
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_t A
cmark_lt H_{c}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline 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:  point I is not incident to the line c
% Constructing a point P_{\_G19446} which is a foot of the point I on the line c
foot P_{\_G19446} I c 
cmark_r P_{\_G19446}
color 200 200 200
drawline I P_{\_G19446} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G19446}
circle k(I,P_{a}) I P_{\_G19446} 

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 a point P_{\_G19653} which is a foot of the point I on the line c
foot P_{\_G19653} I c 
cmark_r P_{\_G19653}
color 200 200 200
drawline I P_{\_G19653} 
color 0 0 0

% Constructing a line L_{\_G19656} which passes through point I and point A
line L_{\_G19656} I A 

color 200 200 200
drawline L_{\_G19656}
color 0 0 0


% Constructing a point P_{\_G19659} which is an image of the point P_{\_G19653} in the symmetry to point/line L_{\_G19656}
sim P_{\_G19659} L_{\_G19656} P_{\_G19653} 
cmark_r P_{\_G19659}

% Constructing a line b which passes through point A and point P_{\_G19659}
line b A P_{\_G19659} 

color 200 200 200
drawline b
color 0 0 0



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


% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G20045} which is a foot of the point I on the line b
foot P_{\_G20045} I b 
cmark_r P_{\_G20045}
color 200 200 200
drawline I P_{\_G20045} 
color 0 0 0

% Constructing a line L_{\_G20048} which passes through point I and point C
line L_{\_G20048} I C 

color 200 200 200
drawline L_{\_G20048}
color 0 0 0


% Constructing a point P_{\_G20051} which is an image of the point P_{\_G20045} in the symmetry to point/line L_{\_G20048}
sim P_{\_G20051} L_{\_G20048} P_{\_G20045} 
cmark_r P_{\_G20051}

% Constructing a line a which passes through point C and point P_{\_G20051}
line a C P_{\_G20051} 

color 200 200 200
drawline a
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



drawsegment A B
drawsegment A C
drawsegment B C

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