Construction in GCLC language
dim 120 120
point E_{c} 95 56.36
point H 80 72.73
point T_{c} 55.38 72.43
color 220 0 0
fontsize 11
cmark_r E_{c}
cmark_rt H
cmark_lt T_{c}
color 0 0 0
fontsize 10
% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1
cmark_b C
color 200 200 200
drawsegment H C
color 0 0 0
% DET: points E_{c} and H are not the same
% Constructing a line h_{c} which passes through point E_{c} and point H
line h_{c} E_{c} H
color 200 200 200
drawline h_{c}
color 0 0 0
% DET: points T_{c} and C are not the same
% Constructing a line s_{c} which passes through point T_{c} and point C
line s_{c} T_{c} C
color 200 200 200
drawline s_{c}
color 0 0 0
% Constructing a line c which is perpendicular to line h_{c} and which passes through point T_{c}
perp c T_{c} h_{c}
color 200 200 200
drawline c
color 0 0 0
% NDG: lines c and h_{c} are not parallel% DET: lines c and h_{c} are not the same
% Constructing a point H_{c} which belongs to line c and line h_{c}
intersec H_{c} c h_{c}
cmark_lt H_{c}
% DET: points H and H_{c} are not the same
% Constructing bisector m(HH_{c}) of the segment HH_{c}
med m(HH_{c}) H H_{c}
color 200 200 200
drawline m(HH_{c})
color 0 0 0
color 200 200 200
drawsegment H H_{c}
color 0 0 0
% NDG: points C and T_{c} are not the same; points E_{c} and C are not the same% DET: points C and T_{c} are not the same
% Constructing an angle V[_G42575] which is equal to the angle E_{c}CT_{c}
angle_o V[_G42575] E_{c} C T_{c}
% Calculating value angle[_G42654] using formula 1/pow(2,0)*V[_G42575]+0/pow(2,0)*180
expression angle[_G42654] { 1/pow(2,0)*V[_G42575]+0/pow(2,0)*180 }
% Constructing a point P_{\_G42651} which is an image of the point T_{c} in a rotation around the point C for the angle 1/pow(2,0)*V[_G42575]+0/pow(2,0)*180
rotate P_{\_G42651} C angle[_G42654] T_{c}
cmark_r P_{\_G42651}
color 200 200 200
drawarc_p C T_{c} angle[_G42654]
color 0 0 0
% Constructing a line CO which passes through point C and point P_{\_G42651}
line CO C P_{\_G42651}
color 200 200 200
drawline CO
color 0 0 0
% Constructing a line m(H_{b}H_{a}) which contains the point E_{c} and is parallel to the line CO
parallel m(H_{b}H_{a}) E_{c} CO
color 200 200 200
drawline m(H_{b}H_{a})
color 0 0 0
% NDG: lines m(H_{b}H_{a}) and c are not parallel% DET: lines m(H_{b}H_{a}) and c are not the same
% Constructing a point M_{c} which belongs to line m(H_{b}H_{a}) and line c
intersec M_{c} m(H_{b}H_{a}) c
cmark_lt M_{c}
% Constructing a line L_{\_G43170} which passes through point M_{c} and point C
line L_{\_G43170} M_{c} C
color 200 200 200
drawline L_{\_G43170}
color 0 0 0
% Constructing a point P_{\_G43271} with coordinates (0,0)
point P_{\_G43271} 0 0
cmark_r P_{\_G43271}
% Constructing a point P_{\_G43195} such that M_{c}P_{\_G43195}/M_{c}P_{\_G43271}=1
towards P_{\_G43195} M_{c} P_{\_G43271} 1
cmark_r P_{\_G43195}
color 200 200 200
drawsegment M_{c} P_{\_G43195}
color 0 0 0
% Constructing a point P_{\_G43240} such that M_{c}P_{\_G43240}/M_{c}P_{\_G43271}=3
towards P_{\_G43240} M_{c} P_{\_G43271} 3
cmark_r P_{\_G43240}
color 200 200 200
drawsegment M_{c} P_{\_G43240}
color 0 0 0
% Constructing a line L_{\_G43201} which passes through point C and point P_{\_G43240}
line L_{\_G43201} C P_{\_G43240}
color 200 200 200
drawline L_{\_G43201}
color 0 0 0
% Constructing a line L_{\_G43164} which contains the point P_{\_G43195} and is parallel to the line L_{\_G43201}
parallel L_{\_G43164} P_{\_G43195} L_{\_G43201}
color 200 200 200
drawline L_{\_G43164}
color 0 0 0
% Constructing a point G which belongs to line L_{\_G43164} and line L_{\_G43170}
intersec G L_{\_G43164} L_{\_G43170}
cmark_t G
% Constructing a point N such that HN/HG=0.75
towards N H G 0.75
cmark_r N
color 200 200 200
drawsegment H G
color 0 0 0
% NDG: points E_{c} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{c}
circle k(N,M_{a}) N E_{c}
color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0
% NDG: line m(HH_{c}) and circle k(N,M_{a}) intersect
% Constructing points E_{a} and E_{b} which are in intersection of k(N,M_{a}) and m(HH_{c})
intersec2 E_{a} E_{b} k(N,M_{a}) m(HH_{c})
cmark_r E_{a}
cmark_r E_{b}
% Constructing a point A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1
cmark_t A
color 200 200 200
drawsegment H A
color 0 0 0
% Constructing a point B such that HB/HE_{b}=2
towards B H E_{b} 2
cmark_b B
color 200 200 200
drawsegment H B
color 0 0 0
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: line m(HH_{c}) and circle k(N,M_{a}) intersect; points E_{c} and N are not the same; lines m(H_{b}H_{a}) and c are not parallel; points C and T_{c} are not the same; points E_{c} and C are not the same; lines c and h_{c} are not parallel
% Determination conditions: lines m(H_{b}H_{a}) and c are not the same; points C and T_{c} are not the same; points H and H_{c} are not the same; lines c and h_{c} are not the same; points T_{c} and C are not the same; points E_{c} and H are not the same