Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point G 70 58.33
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_t G
cmark_b I
color 0 0 0
fontsize 10


% Constructing a point B such that M_{b}B/M_{b}G=3
towards B M_{b} G 3 
cmark_b B
color 200 200 200
drawsegment M_{b} 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



% 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:  points I and M_{b} are not the same
% Constructing midpoint P_{\_G48213} of the segment IM_{b}
midpoint P_{\_G48213} I M_{b} 
cmark_r P_{\_G48213}

% Constructing a circle k_over(I,M_{b}) whose center is at point P_{\_G48213} and which passes through point I
circle k_over(I,M_{b}) P_{\_G48213} I 

color 200 200 200
drawcircle k_over(I,M_{b})
color 0 0 0




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

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




% Constructing a point P_{\_G48514} such that M_{b}P_{\_G48514}/M_{b}B=-1
towards P_{\_G48514} M_{b} B -1 
cmark_r P_{\_G48514}
color 200 200 200
drawsegment B P_{\_G48514} 
color 0 0 0

% Constructing a line h_{M_{b},-1/1}(BP`_{b}) which contains the point P_{\_G48514} and is parallel to the line BP`_{b}
parallel h_{M_{b},-1/1}(BP`_{b}) P_{\_G48514} BP`_{b} 

color 200 200 200
drawline h_{M_{b},-1/1}(BP`_{b})
color 0 0 0



% NDG:  line h_{M_{b},-1/1}(BP`_{b}) and circle k_over(I,M_{b}) intersect
% Constructing points B_{fo} and P_{b} which are in intersection of k_over(I,M_{b}) and h_{M_{b},-1/1}(BP`_{b})
intersec2 B_{fo} P_{b} k_over(I,M_{b}) h_{M_{b},-1/1}(BP`_{b}) 
cmark_r B_{fo}
cmark_r P_{b}


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

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



% NDG:  point M_{b} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G49263} of the segment M_{b}I
midpoint P_{\_G49263} M_{b} I 
cmark_r P_{\_G49263}

% Constructing a circle C_{\_G49266} whose center is at point P_{\_G49263} and which passes through point M_{b}
circle C_{\_G49266} P_{\_G49263} M_{b} 

color 200 200 200
drawcircle C_{\_G49266}
color 0 0 0


% Constructing points P_{\_G49269} and P_{\_G49272} which are in intersection of C_{\_G49266} and k(I,P_{a})
intersec2 P_{\_G49269} P_{\_G49272} C_{\_G49266} k(I,P_{a}) 
cmark_r P_{\_G49269}
cmark_r P_{\_G49272}

% Constructing a line x2 which passes through point M_{b} and point P_{\_G49269}
line x2 M_{b} P_{\_G49269} 

color 200 200 200
drawline x2
color 0 0 0


% Constructing a line b which passes through point M_{b} and point P_{\_G49272}
line b M_{b} P_{\_G49272} 

color 200 200 200
drawline 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



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; point M_{b} is outside the circle k(I,P_{a}); points P_{b} and I are not the same; line h_{M_{b},-1/1}(BP`_{b}) and circle k_over(I,M_{b}) intersect; 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; points M_{b} and I are not the same