Construction in GCLC language

dim 120 120

point M_{a} 65 40
point T_{a} 70.86 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b M_{a}
cmark_b T_{a}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawline s_{a}
color 0 0 0




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

color 200 200 200
drawline m_{a}
color 0 0 0



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


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

color 200 200 200
drawcircle k(N_{a},C)
color 0 0 0



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


% NDG:  point I is not incident to the line a
% Constructing a point P_{\_G56774} which is a foot of the point I on the line a
foot P_{\_G56774} I a 
cmark_r P_{\_G56774}
color 200 200 200
drawline I P_{\_G56774} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G56774}
circle k(I,P_{a}) I P_{\_G56774} 

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_{\_G56981} which is a foot of the point I on the line a
foot P_{\_G56981} I a 
cmark_r P_{\_G56981}
color 200 200 200
drawline I P_{\_G56981} 
color 0 0 0

% Constructing a line L_{\_G56984} which passes through point I and point C
line L_{\_G56984} I C 

color 200 200 200
drawline L_{\_G56984}
color 0 0 0


% Constructing a point P_{\_G56987} which is an image of the point P_{\_G56981} in the symmetry to point/line L_{\_G56984}
sim P_{\_G56987} L_{\_G56984} P_{\_G56981} 
cmark_r P_{\_G56987}

% Constructing a line b which passes through point C and point P_{\_G56987}
line b C P_{\_G56987} 

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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