Construction in GCLC language

dim 120 120

point M_{a} 65 40
point H_{a} 80 40
point I 74.37 61.15

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawline IM_{a}
color 0 0 0



% NDG:  points I and M_{a} are not the same
% Constructing midpoint P_{\_G52760} of the segment IM_{a}
midpoint P_{\_G52760} I M_{a} 
cmark_r P_{\_G52760}

% Constructing a circle k_over(I,M_{a}) whose center is at point P_{\_G52760} and which passes through point I
circle k_over(I,M_{a}) P_{\_G52760} I 

color 200 200 200
drawcircle k_over(I,M_{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




% 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_{\_G53058} which is a foot of the point I on the line a
foot P_{\_G53058} I a 
cmark_r P_{\_G53058}
color 200 200 200
drawline I P_{\_G53058} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G53058}
circle k(I,P_{a}) I P_{\_G53058} 

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



% NDG:  circles k(I,P_{a}) and k_over(I,M_{a}) intersect% DET:  circles k(I,P_{a}) and k_over(I,M_{a}) are not the same
% Constructing points P_{a} and A_{fi} which are in intersection of k(I,P_{a}) and k_over(I,M_{a})
intersec2 P_{a} A_{fi} k(I,P_{a}) k_over(I,M_{a}) 
cmark_r P_{a}
cmark_r A_{fi}



% Constructing a point P`_{a} such that P_{a}P`_{a}/P_{a}M_{a}=2
towards P`_{a} P_{a} M_{a} 2 
cmark_r P`_{a}
color 200 200 200
drawsegment P_{a} P`_{a} 
color 0 0 0



% Constructing a line AP`_{a} which contains the point P`_{a} and is parallel to the line IM_{a}
parallel AP`_{a} P`_{a} IM_{a} 

color 200 200 200
drawline AP`_{a}
color 0 0 0



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


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

color 200 200 200
drawline s_{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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  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; lines AP`_{a} and h_{a} are not parallel; circles k(I,P_{a}) and k_over(I,M_{a}) intersect; point I is not incident to the line a; points I and M_{a} are not the same
% Determination conditions:  lines m_{a} and s_{a} are not the same; points I and A are not the same; lines AP`_{a} and h_{a} are not the same; circles k(I,P_{a}) and k_over(I,M_{a}) are not the same; points M_{a} and I are not the same; points M_{a} and H_{a} are not the same