Construction in GCLC language

dim 120 120

point C 110 40
point H_{c} 68.91 84.83
point I 74.37 61.15

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline h_{c}
color 0 0 0




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

color 200 200 200
drawline c
color 0 0 0



% NDG:  point I is not incident to the line c
% Constructing a point P_{\_G31357} which is a foot of the point I on the line c
foot P_{\_G31357} I c 
cmark_r P_{\_G31357}
color 200 200 200
drawline I P_{\_G31357} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G31357}
circle k(I,P_{a}) I P_{\_G31357} 

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 midpoint P_{\_G31591} of the segment CI
midpoint P_{\_G31591} C I 
cmark_r P_{\_G31591}

% Constructing a circle C_{\_G31594} whose center is at point P_{\_G31591} and which passes through point C
circle C_{\_G31594} P_{\_G31591} C 

color 200 200 200
drawcircle C_{\_G31594}
color 0 0 0


% Constructing points P_{\_G31597} and P_{\_G31600} which are in intersection of C_{\_G31594} and k(I,P_{a})
intersec2 P_{\_G31597} P_{\_G31600} C_{\_G31594} k(I,P_{a}) 
cmark_r P_{\_G31597}
cmark_r P_{\_G31600}

% Constructing a line a which passes through point C and point P_{\_G31597}
line a C P_{\_G31597} 

color 200 200 200
drawline a
color 0 0 0


% Constructing a line b which passes through point C and point P_{\_G31600}
line b C P_{\_G31600} 

color 200 200 200
drawline b
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


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



drawsegment A B
drawsegment A C
drawsegment B C

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