Construction in GCLC language

dim 120 120

point C 110 40
point H_{a} 80 40
point I 74.37 61.15

color 220 0 0
fontsize 11

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

% DET:  points C and H_{a} are not the same
% Constructing a line a which passes through point C and point H_{a}
line a C 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_{\_G34324} which is a foot of the point I on the line a
foot P_{\_G34324} I a 
cmark_r P_{\_G34324}
color 200 200 200
drawline I P_{\_G34324} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G34324}
circle k(I,P_{a}) I P_{\_G34324} 

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



% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G34531} which is a foot of the point I on the line a
foot P_{\_G34531} I a 
cmark_r P_{\_G34531}
color 200 200 200
drawline I P_{\_G34531} 
color 0 0 0

% Constructing a line L_{\_G34534} which passes through point I and point C
line L_{\_G34534} I C 

color 200 200 200
drawline L_{\_G34534}
color 0 0 0


% Constructing a point P_{\_G34537} which is an image of the point P_{\_G34531} in the symmetry to point/line L_{\_G34534}
sim P_{\_G34537} L_{\_G34534} P_{\_G34531} 
cmark_r P_{\_G34537}

% Constructing a line b which passes through point C and point P_{\_G34537}
line b C P_{\_G34537} 

color 200 200 200
drawline b
color 0 0 0



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


% NDG:  point A is outside the circle k(I,P_{a})
% Constructing a point P_{\_G34923} which is a foot of the point I on the line b
foot P_{\_G34923} I b 
cmark_r P_{\_G34923}
color 200 200 200
drawline I P_{\_G34923} 
color 0 0 0

% Constructing a line L_{\_G34926} which passes through point I and point A
line L_{\_G34926} I A 

color 200 200 200
drawline L_{\_G34926}
color 0 0 0


% Constructing a point P_{\_G34929} which is an image of the point P_{\_G34923} in the symmetry to point/line L_{\_G34926}
sim P_{\_G34929} L_{\_G34926} P_{\_G34923} 
cmark_r P_{\_G34929}

% Constructing a line c which passes through point A and point P_{\_G34929}
line c A P_{\_G34929} 

color 200 200 200
drawline c
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



drawsegment A B
drawsegment A C
drawsegment B C

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