## Re: X(5446) & X(5447): Pending coordinates

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• Thanks Cesar! It turns out X(5446) is the midpoint of X(4) and X(52), and also the reflection of X(1216) in X(5), and the reflection of X(389) in X(143). It
Message 1 of 2 , Apr 11, 2013
Thanks Cesar!

It turns out X(5446) is the midpoint of X(4) and X(52), and also the reflection of X(1216) in X(5), and the reflection of X(389) in X(143).
It also lies on lines (at least) 2,5447 5,1216 22,569 23,54 25,1147 143,389 155,1351.

I had found these trilinears for X(5446): 2R^2 cos A - a^2 cos(B - C). I used this to find a bit messier trilinears for X(5447) using the complement function, but yours are much cleaner.

X(5447) is also the midpoint of X(3) and X(1216), and lies on (at least) these lines: 2,5446 3,49 5,3819 51,3526 52,631 140,143.

Another related center that may be interesting:
{X(3),X(51)}-harmonic conjugate of X(5446)
Trilinears 2R^2 cos A + a^2 cos(B - C) : :
= complement of X(1216)
= midpoint of X(5) and X(389)
= midpoint of X(140) and X(143)
= {X(2),X(52)}-harmonic conjugate of X(1216)
= {X(24),X(5422)}-harmonic conjugate of X(569)
= ETC search 1.786059910579708
lies on lines (at least) 2,52 3,51 4,4846 5,389 6,1147 24,569 140,143 155,5020 185,381 195,3292.

Randy

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> X(5446) = INTERSECTION OF LINES X(371)X(5417) AND X(372)X(5419)
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> Coordinates (pending)
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> The first attempt was done intersecting lines X(371)X(5417) and
> X(372)X(5419).
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> This produced the not nice trilinears
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> G(A,B,C) : G(B,C,A) : G(C,A,B)
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> where G(A,B,C)=
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> (4-4*cos(2*B)+cos(2*B-2*C)-4*cos(2*C)+5*cos(2*A))*(2*cos(B-C)*(-1+cos(2*A))+
> 2*cos(A))*(2*cos(B-C)*(3-2*cos(2*A)+sin(2*A))+cos(A)-cos(3*A)+6*sin(A))*(-2*
> cos(B-C)*(-3+2*cos(2*A)+sin(2*A))+cos(A)-cos(3*A)-6*sin(A))
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> Using this center function it was possible to determine that X(5446) is also
> on lines X(3)X(51) and X(4)X(52).
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> With these last two lines it is possible to find a nicer expression for
> trilinears of X(5446)
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> F(A,B,C) : F(B,C,A) : F(C,A,B),
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> where F(A,B,C) =cos(2*A)*cos(B-C) - 2*cos(B)*cos(C)
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> X(5447) = COMPLEMENT OF X(5446)
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> Coordinates (pending)
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> Trilinears: F(A,B,C) : F(B,C,A) : F(C,A,B)
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> where F(A,B,C)=cos(A)*( cos(2*B) + cos(2*C) - 3)
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> Regards
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> [Non-text portions of this message have been removed]
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