Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point H_{b} 89.36 77.83
point I 74.37 61.15

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline IM_{b}
color 0 0 0



% NDG:  points I and M_{b} are not the same
% Constructing midpoint P_{\_G64882} of the segment IM_{b}
midpoint P_{\_G64882} I M_{b} 
cmark_r P_{\_G64882}

% Constructing a circle k_over(I,M_{b}) whose center is at point P_{\_G64882} and which passes through point I
circle k_over(I,M_{b}) P_{\_G64882} I 

color 200 200 200
drawcircle k_over(I,M_{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




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

color 200 200 200
drawline h_{b}
color 0 0 0



% NDG:  point I is not incident to the line b
% Constructing a point P_{\_G40013} which is a foot of the point I on the line b
foot P_{\_G40013} I b 
cmark_r P_{\_G40013}
color 200 200 200
drawline I P_{\_G40013} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G40013}
circle k(I,P_{a}) I P_{\_G40013} 

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



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



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



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

color 200 200 200
drawline BP`_{b}
color 0 0 0



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


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

color 200 200 200
drawline s_{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



drawsegment A B
drawsegment A C
drawsegment B C

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