Construction in GCLC language

dim 120 120

point B 20 40
point H_{c} 68.91 84.83
point I 74.37 61.15

color 220 0 0
fontsize 11

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

% DET:  points B and H_{c} are not the same
% Constructing a line c which passes through point B and point H_{c}
line c B 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_{\_G53019} which is a foot of the point I on the line c
foot P_{\_G53019} I c 
cmark_r P_{\_G53019}
color 200 200 200
drawline I P_{\_G53019} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G53019}
circle k(I,P_{a}) I P_{\_G53019} 

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_{\_G53226} which is a foot of the point I on the line c
foot P_{\_G53226} I c 
cmark_r P_{\_G53226}
color 200 200 200
drawline I P_{\_G53226} 
color 0 0 0

% Constructing a line L_{\_G53229} which passes through point I and point B
line L_{\_G53229} I B 

color 200 200 200
drawline L_{\_G53229}
color 0 0 0


% Constructing a point P_{\_G53232} which is an image of the point P_{\_G53226} in the symmetry to point/line L_{\_G53229}
sim P_{\_G53232} L_{\_G53229} P_{\_G53226} 
cmark_r P_{\_G53232}

% Constructing a line a which passes through point B and point P_{\_G53232}
line a B P_{\_G53232} 

color 200 200 200
drawline a
color 0 0 0



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


% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G53618} which is a foot of the point I on the line a
foot P_{\_G53618} I a 
cmark_r P_{\_G53618}
color 200 200 200
drawline I P_{\_G53618} 
color 0 0 0

% Constructing a line L_{\_G53621} which passes through point I and point C
line L_{\_G53621} I C 

color 200 200 200
drawline L_{\_G53621}
color 0 0 0


% Constructing a point P_{\_G53624} which is an image of the point P_{\_G53618} in the symmetry to point/line L_{\_G53621}
sim P_{\_G53624} L_{\_G53621} P_{\_G53618} 
cmark_r P_{\_G53624}

% Constructing a line b which passes through point C and point P_{\_G53624}
line b C P_{\_G53624} 

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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