Construction in GCLC language
dim 120 120
point B 20 40
point H_{a} 80 40
point N 72.5 61.93
color 220 0 0
fontsize 11
cmark_b B
cmark_b H_{a}
cmark_r N
color 0 0 0
fontsize 10
% DET: points B and H_{a} are not the same
% Constructing a line a which passes through point B and point H_{a}
line a B H_{a}
color 200 200 200
drawline a
color 0 0 0
% NDG: points H_{a} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point H_{a}
circle k(N,M_{a}) N H_{a}
color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0
% NDG: line a and circle k(N,M_{a}) intersect% DET: points H_{a} and M_{a} must be different
% Constructing a point P_{\_G29238} which is a foot of the point N on the line a
foot P_{\_G29238} N a
cmark_r P_{\_G29238}
color 200 200 200
drawline N P_{\_G29238}
color 0 0 0
% Constructing a point M_{a} which is an image of the point H_{a} in the symmetry to point/line P_{\_G29238}
sim M_{a} P_{\_G29238} H_{a}
cmark_b M_{a}
% Constructing a point C such that M_{a}C/M_{a}B=-1
towards C M_{a} B -1
cmark_b C
color 200 200 200
drawsegment B C
color 0 0 0
% DET: points N and M_{a} are not the same
% Constructing a line m(H_{b}H_{c}) which passes through point N and point M_{a}
line m(H_{b}H_{c}) N M_{a}
color 200 200 200
drawline m(H_{b}H_{c})
color 0 0 0
% NDG: line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect% DET: points M_{a} and E_{a} must be different
% Constructing a point E_{a} which is an image of the point M_{a} in the symmetry to point/line N
sim E_{a} N M_{a}
cmark_r E_{a}
% DET: points E_{a} and H_{a} are not the same
% Constructing a line h_{a} which passes through point E_{a} and point H_{a}
line h_{a} E_{a} H_{a}
color 200 200 200
drawline h_{a}
color 0 0 0
% NDG: points B and M_{a} are not the same
% Constructing a circle k(M_{a},B) whose center is at point M_{a} and which passes through point B
circle k(M_{a},B) M_{a} B
color 200 200 200
drawcircle k(M_{a},B)
color 0 0 0
% NDG: circles k(N,M_{a}) and k(M_{a},B) intersect% DET: circles k(N,M_{a}) and k(M_{a},B) are not the same
% Constructing points H_{b} and H_{c} which are in intersection of k(N,M_{a}) and k(M_{a},B)
intersec2 H_{b} H_{c} k(N,M_{a}) k(M_{a},B)
cmark_rt H_{b}
cmark_lt H_{c}
% DET: points B and H_{b} are not the same
% Constructing a line h_{b} which passes through point B and point H_{b}
line h_{b} B H_{b}
color 200 200 200
drawline h_{b}
color 0 0 0
% NDG: lines h_{a} and h_{b} are not parallel% DET: lines h_{a} and h_{b} are not the same
% Constructing a point H which belongs to line h_{a} and line h_{b}
intersec H h_{a} h_{b}
cmark_rt H
% Constructing a line L_{\_G30036} which passes through point N and point H
line L_{\_G30036} N H
color 200 200 200
drawline L_{\_G30036}
color 0 0 0
% Constructing a point P_{\_G30137} with coordinates (0,0)
point P_{\_G30137} 0 0
cmark_r P_{\_G30137}
% Constructing a point P_{\_G30061} such that NP_{\_G30061}/NP_{\_G30137}=-1
towards P_{\_G30061} N P_{\_G30137} -1
cmark_r P_{\_G30061}
color 200 200 200
drawsegment P_{\_G30137} P_{\_G30061}
color 0 0 0
% Constructing a point P_{\_G30106} such that NP_{\_G30106}/NP_{\_G30137}=3
towards P_{\_G30106} N P_{\_G30137} 3
cmark_r P_{\_G30106}
color 200 200 200
drawsegment N P_{\_G30106}
color 0 0 0
% Constructing a line L_{\_G30067} which passes through point H and point P_{\_G30106}
line L_{\_G30067} H P_{\_G30106}
color 200 200 200
drawline L_{\_G30067}
color 0 0 0
% Constructing a line L_{\_G30030} which contains the point P_{\_G30061} and is parallel to the line L_{\_G30067}
parallel L_{\_G30030} P_{\_G30061} L_{\_G30067}
color 200 200 200
drawline L_{\_G30030}
color 0 0 0
% Constructing a point G which belongs to line L_{\_G30030} and line L_{\_G30036}
intersec G L_{\_G30030} L_{\_G30036}
cmark_t G
% Constructing a point A such that M_{a}A/M_{a}G=3
towards A M_{a} G 3
cmark_t A
color 200 200 200
drawsegment M_{a} A
color 0 0 0
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines h_{a} and h_{b} are not parallel; circles k(N,M_{a}) and k(M_{a},B) intersect; points B and M_{a} are not the same; line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect; line a and circle k(N,M_{a}) intersect; points H_{a} and N are not the same
% Determination conditions: lines h_{a} and h_{b} are not the same; points B and H_{b} are not the same; circles k(N,M_{a}) and k(M_{a},B) are not the same; points E_{a} and H_{a} are not the same; points M_{a} and E_{a} must be different; points N and M_{a} are not the same; points H_{a} and M_{a} must be different; points B and H_{a} are not the same