HYACINTHOS 26805

 

Q( X(1), X(4614) ) = Infinity point of line X(1)X(4822): This point is now X(15309) in ETC

Q( X(1), X(8851) ) = Infinity point of line X(44)X(573): This point is now X(15310) in ETC

Q( X(4), X(14944) ) = Infinity point of line X(4)X(253): This point is now X(15312) in ETC

 

Isogonal  conjugate of  X(15309)

= a*(a-b)*(a-c)*(a^2+(3*b+2*c) *a+(b+c)^2)*(a^2+(2*b+3*c)*a+( b+c)^2) : :  (barys)

= on the circumcircle and these lines: {100, 4115}, {111, 612}, {386, 741}, {662, 6578}, {4614, 15309}

= isogonal conjugate of X(15309)

= trilinear pole of the line {6, 1962}

= [ 2.457239526239436, -1.46766510649104, 3.522629774290743 ]

 

Isogonal  conjugate of  X(15310)

= ((b-c)*a^4-b^2*a^3-(b^3-b*c^ 2-c^3)*a^2+b*(b-c)*(b^2+b*c+2* c^2)*a-(b^2-c^2)*c*b^2)*((b-c) *a^4+c^2*a^3-(b^3+b^2*c-c^3)* a^2+c*(b-c)*(2*b^2+b*c+c^2)*a- (b^2-c^2)*b*c^2)*a : :  (barys)

= on the circumcircle and these lines: {3, 932}, {4, 5518}, {100, 11689}, {101, 3501}, {108, 1403}, {109, 3550}, {110, 13588}, {1292, 11491}, {3651, 6010}, {6360, 13397}, {8851, 15310}

= reflection of X(i) in X(j) for these (i,j): (4, 5518), (932, 3)

= isogonal conjugate of X(15310)

= antipode of X(932) in the circumcircle

= [ 2.457239526239436, -1.46766510649104, 3.522629774290743 ]

 

Isogonal  conjugate of  X(15312)

= f(SB)*f(SC) : f(SC)*f(SA) : f(SA)*f(SB)  (barys), where f(SA)=2*S^4-(SA-SW)*(16*R^2-3* SA-4*SW)*S^2+4*(4*R^2-SW)*(SA- SW)*SA*SW

= on the circumcircle and these lines: {4, 13613}, {107, 3079}, {108, 8807}, {110, 6617}, {112, 1498}, {154, 1301}, {2764, 12096}

= reflection of X(4) in X(13613)

= isogonal conjugate of X(15312)

= [ 10.439279728833270, 13.31052346381911, -10.392442406351900 ]

 

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