[Antreas P. Hatzipolakis]:
2 a^15-a^14 b-a^13 b^2+a^12 b^3-10 a^11 b^4-3 a^10 b^5+11 a^9 b^6+19 a^8 b^7+6 a^7 b^8-31 a^6 b^9-11 a^5 b^10+15 a^4 b^11+2 a^3 b^12+3 a^2 b^13+a b^14-3 b^15-a^14 c+7 a^10 b^4 c+12 a^9 b^5 c-20 a^8 b^6 c-32 a^7 b^7 c+29 a^6 b^8 c+24 a^5 b^9 c-16 a^4 b^10 c-3 a^2 b^12 c-4 a b^13 c+4 b^14 c-a^13 c^2+20 a^11 b^2 c^2-4 a^10 b^3 c^2-11 a^9 b^4 c^2-34 a^8 b^5 c^2-16 a^7 b^6 c^2+56 a^6 b^7 c^2-7 a^5 b^8 c^2+12 a^4 b^9 c^2+12 a^3 b^10 c^2-36 a^2 b^11 c^2+3 a b^12 c^2+6 b^13 c^2+a^12 c^3-4 a^10 b^2 c^3-24 a^9 b^3 c^3+35 a^8 b^4 c^3+32 a^7 b^5 c^3-48 a^6 b^6 c^3+16 a^5 b^7 c^3-9 a^4 b^8 c^3-32 a^3 b^9 c^3+36 a^2 b^10 c^3+8 a b^11 c^3-11 b^12 c^3-10 a^11 c^4+7 a^10 b c^4-11 a^9 b^2 c^4+35 a^8 b^3 c^4+20 a^7 b^4 c^4-6 a^6 b^5 c^4+18 a^5 b^6 c^4-110 a^4 b^7 c^4-2 a^3 b^8 c^4+63 a^2 b^9 c^4-15 a b^10 c^4+11 b^11 c^4-3 a^10 c^5+12 a^9 b c^5-34 a^8 b^2 c^5+32 a^7 b^3 c^5-6 a^6 b^4 c^5-80 a^5 b^5 c^5+108 a^4 b^6 c^5+32 a^3 b^7 c^5-63 a^2 b^8 c^5+4 a b^9 c^5-2 b^10 c^5+11 a^9 c^6-20 a^8 b c^6-16 a^7 b^2 c^6-48 a^6 b^3 c^6+18 a^5 b^4 c^6+108 a^4 b^5 c^6-24 a^3 b^6 c^6+11 a b^8 c^6-40 b^9 c^6+19 a^8 c^7-32 a^7 b c^7+56 a^6 b^2 c^7+16 a^5 b^3 c^7-110 a^4 b^4 c^7+32 a^3 b^5 c^7-16 a b^7 c^7+35 b^8 c^7+6 a^7 c^8+29 a^6 b c^8-7 a^5 b^2 c^8-9 a^4 b^3 c^8-2 a^3 b^4 c^8-63 a^2 b^5 c^8+11 a b^6 c^8+35 b^7 c^8-31 a^6 c^9+24 a^5 b c^9+12 a^4 b^2 c^9-32 a^3 b^3 c^9+63 a^2 b^4 c^9+4 a b^5 c^9-40 b^6 c^9-11 a^5 c^10-16 a^4 b c^10+12 a^3 b^2 c^10+36 a^2 b^3 c^10-15 a b^4 c^10-2 b^5 c^10+15 a^4 c^11-36 a^2 b^2 c^11+8 a b^3 c^11+11 b^4 c^11+2 a^3 c^12-3 a^2 b c^12+3 a b^2 c^12-11 b^3 c^12+3 a^2 c^13-4 a b c^13+6 b^2 c^13+a c^14+4 b c^14-3 c^15::
Let ABC be a triangle and A'B'C' the pedal triangle of I.
Denote:
A" = AH /\ B'C'
B" = BH /\ C'A'
C" = CH /\ A'B'
The NPCs of A"HI, B"HI, C"HI are coaxial.
2nd, other than the midpoint of HI, intersection?
[Peter Moses]:
Hi Antreas,
Denote:
A" = AH /\ B'C'
B" = BH /\ C'A'
C" = CH /\ A'B'
The NPCs of A"HI, B"HI, C"HI are coaxial.
2nd, other than the midpoint of HI, intersection?
[Peter Moses]:
Hi Antreas,
>2nd, other than the midpoint of HI, intersection?
2 a^15-a^14 b-a^13 b^2+a^12 b^3-10 a^11 b^4-3 a^10 b^5+11 a^9 b^6+19 a^8 b^7+6 a^7 b^8-31 a^6 b^9-11 a^5 b^10+15 a^4 b^11+2 a^3 b^12+3 a^2 b^13+a b^14-3 b^15-a^14 c+7 a^10 b^4 c+12 a^9 b^5 c-20 a^8 b^6 c-32 a^7 b^7 c+29 a^6 b^8 c+24 a^5 b^9 c-16 a^4 b^10 c-3 a^2 b^12 c-4 a b^13 c+4 b^14 c-a^13 c^2+20 a^11 b^2 c^2-4 a^10 b^3 c^2-11 a^9 b^4 c^2-34 a^8 b^5 c^2-16 a^7 b^6 c^2+56 a^6 b^7 c^2-7 a^5 b^8 c^2+12 a^4 b^9 c^2+12 a^3 b^10 c^2-36 a^2 b^11 c^2+3 a b^12 c^2+6 b^13 c^2+a^12 c^3-4 a^10 b^2 c^3-24 a^9 b^3 c^3+35 a^8 b^4 c^3+32 a^7 b^5 c^3-48 a^6 b^6 c^3+16 a^5 b^7 c^3-9 a^4 b^8 c^3-32 a^3 b^9 c^3+36 a^2 b^10 c^3+8 a b^11 c^3-11 b^12 c^3-10 a^11 c^4+7 a^10 b c^4-11 a^9 b^2 c^4+35 a^8 b^3 c^4+20 a^7 b^4 c^4-6 a^6 b^5 c^4+18 a^5 b^6 c^4-110 a^4 b^7 c^4-2 a^3 b^8 c^4+63 a^2 b^9 c^4-15 a b^10 c^4+11 b^11 c^4-3 a^10 c^5+12 a^9 b c^5-34 a^8 b^2 c^5+32 a^7 b^3 c^5-6 a^6 b^4 c^5-80 a^5 b^5 c^5+108 a^4 b^6 c^5+32 a^3 b^7 c^5-63 a^2 b^8 c^5+4 a b^9 c^5-2 b^10 c^5+11 a^9 c^6-20 a^8 b c^6-16 a^7 b^2 c^6-48 a^6 b^3 c^6+18 a^5 b^4 c^6+108 a^4 b^5 c^6-24 a^3 b^6 c^6+11 a b^8 c^6-40 b^9 c^6+19 a^8 c^7-32 a^7 b c^7+56 a^6 b^2 c^7+16 a^5 b^3 c^7-110 a^4 b^4 c^7+32 a^3 b^5 c^7-16 a b^7 c^7+35 b^8 c^7+6 a^7 c^8+29 a^6 b c^8-7 a^5 b^2 c^8-9 a^4 b^3 c^8-2 a^3 b^4 c^8-63 a^2 b^5 c^8+11 a b^6 c^8+35 b^7 c^8-31 a^6 c^9+24 a^5 b c^9+12 a^4 b^2 c^9-32 a^3 b^3 c^9+63 a^2 b^4 c^9+4 a b^5 c^9-40 b^6 c^9-11 a^5 c^10-16 a^4 b c^10+12 a^3 b^2 c^10+36 a^2 b^3 c^10-15 a b^4 c^10-2 b^5 c^10+15 a^4 c^11-36 a^2 b^2 c^11+8 a b^3 c^11+11 b^4 c^11+2 a^3 c^12-3 a^2 b c^12+3 a b^2 c^12-11 b^3 c^12+3 a^2 c^13-4 a b c^13+6 b^2 c^13+a c^14+4 b c^14-3 c^15::
on lines {{29,102},{2846,14312}}.
Best regards,
Peter Moses.
Best regards,
Peter Moses.
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