Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point H_{a} 80 40
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_b H_{a}
cmark_b T_{a}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



% NDG:  line a and circle k(M_{b},C) intersect% DET:  points H_{a} and C must be different
% Constructing a point P_{\_G61050} which is a foot of the point M_{b} on the line a
foot P_{\_G61050} M_{b} a 
cmark_r P_{\_G61050}
color 200 200 200
drawline M_{b} P_{\_G61050} 
color 0 0 0

% Constructing a point C which is an image of the point H_{a} in the symmetry to point/line P_{\_G61050}
sim C P_{\_G61050} H_{a} 
cmark_b C



% Constructing a point A such that CA/CM_{b}=2
towards A C M_{b} 2 
cmark_t A
color 200 200 200
drawsegment C A 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  point T_{a} is not incident to the line b
% Constructing a point P_{\_G61334} which is a foot of the point T_{a} on the line b
foot P_{\_G61334} T_{a} b 
cmark_r P_{\_G61334}
color 200 200 200
drawline T_{a} P_{\_G61334} 
color 0 0 0

% Constructing a circle k(T_{a},foot[T_{a},c]) whose center is at point T_{a} and which passes through point P_{\_G61334}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G61334} 

color 200 200 200
drawcircle k(T_{a},foot[T_{a},c])
color 0 0 0



% NDG:  point A is outside the circle k(T_{a},foot[T_{a},c])
% Constructing a point P_{\_G61725} which is a foot of the point T_{a} on the line b
foot P_{\_G61725} T_{a} b 
cmark_r P_{\_G61725}
color 200 200 200
drawline T_{a} P_{\_G61725} 
color 0 0 0

% Constructing a line L_{\_G61728} which passes through point T_{a} and point A
line L_{\_G61728} T_{a} A 

color 200 200 200
drawline L_{\_G61728}
color 0 0 0


% Constructing a point P_{\_G61731} which is an image of the point P_{\_G61725} in the symmetry to point/line L_{\_G61728}
sim P_{\_G61731} L_{\_G61728} P_{\_G61725} 
cmark_r P_{\_G61731}

% Constructing a line c which passes through point A and point P_{\_G61731}
line c A P_{\_G61731} 

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(T_{a},foot[T_{a},c]); point T_{a} is not incident to the line b; line a and circle k(M_{b},C) intersect; points H_{a} and M_{b} are not the same
% Determination conditions:  lines c and a are not the same; points M_{b} and C are not the same; points H_{a} and C must be different; points H_{a} and T_{a} are not the same