Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point T_{b} 94.25 68.88
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_rt T_{b}
cmark_b I
color 0 0 0
fontsize 10

% DET:  points M_{b} and T_{b} are not the same
% Constructing a line b which passes through point M_{b} and point T_{b}
line b M_{b} T_{b} 

color 200 200 200
drawline b
color 0 0 0



% DET:  points T_{b} and I are not the same
% Constructing a line s_{b} which passes through point T_{b} and point I
line s_{b} T_{b} I 

color 200 200 200
drawline s_{b}
color 0 0 0




% Constructing a line m_{b} which is perpendicular to line b and which passes through point M_{b}
perp m_{b} M_{b} b 

color 200 200 200
drawline m_{b}
color 0 0 0



% NDG:  lines m_{b} and s_{b} are not parallel% DET:  lines m_{b} and s_{b} are not the same
% Constructing a point N_{b} which belongs to line m_{b} and line s_{b}
intersec N_{b} m_{b} s_{b} 
cmark_rb N_{b}


% NDG:  points I and N_{b} are not the same
% Constructing a circle k(N_{b},A) whose center is at point N_{b} and which passes through point I
circle k(N_{b},A) N_{b} I 

color 200 200 200
drawcircle k(N_{b},A)
color 0 0 0



% NDG:  line b and circle k(N_{b},A) intersect
% Constructing points A and C which are in intersection of k(N_{b},A) and b
intersec2 A C k(N_{b},A) b 
cmark_t A
cmark_b C


% NDG:  point I is not incident to the line b
% Constructing a point P_{\_G48332} which is a foot of the point I on the line b
foot P_{\_G48332} I b 
cmark_r P_{\_G48332}
color 200 200 200
drawline I P_{\_G48332} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G48332}
circle k(I,P_{a}) I P_{\_G48332} 

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_{\_G48539} which is a foot of the point I on the line b
foot P_{\_G48539} I b 
cmark_r P_{\_G48539}
color 200 200 200
drawline I P_{\_G48539} 
color 0 0 0

% Constructing a line L_{\_G48542} which passes through point I and point A
line L_{\_G48542} I A 

color 200 200 200
drawline L_{\_G48542}
color 0 0 0


% Constructing a point P_{\_G48545} which is an image of the point P_{\_G48539} in the symmetry to point/line L_{\_G48542}
sim P_{\_G48545} L_{\_G48542} P_{\_G48539} 
cmark_r P_{\_G48545}

% Constructing a line c which passes through point A and point P_{\_G48545}
line c A P_{\_G48545} 

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines c and s_{b} are not parallel; point A is outside the circle k(I,P_{a}); point I is not incident to the line b; line b and circle k(N_{b},A) intersect; points I and N_{b} are not the same; lines m_{b} and s_{b} are not parallel
% Determination conditions:  lines c and s_{b} are not the same; lines m_{b} and s_{b} are not the same; points T_{b} and I are not the same; points M_{b} and T_{b} are not the same