ADGEOM 4922 * ADGEOM 4923 * ADGEOM 4924

#4922

Dear geometers,

 

I see five concyclic points are

 

X(3), X(187), X(115), X(131) and X(399)

 

Is this circle known before?

 

Best regards,

Tran Quang Hung.

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#4923

Center = X(6132)

Radius = 2*S*R*|OH|*sqrt(|2*S^2*SW -(12*S^2-SW^2)*R^2|)/K, where K=∏(|SB-SC|)

Through ETS’s: {3, 115, 131, 187, 399, 11799, 14981, 15478}

Another:

 

Antipode of X(3) = ISOGONAL CONJUGATE OF X(18878)

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

= 3*X(351)-4*X(6140), 3*X(351)-X(9409), 3*X(351)-2*X(14270), X(3005)-3*X(15451), 4*X(6140)-X(9409), 3*X(15451)-2*X(18117)

= on lines: {3, 6132}, {6, 2510}, {113, 131}, {115, 2971}, {187, 237}, {399, 526}, {523, 11799}, {684, 690}, {804, 6033}, {878, 14601}, {1576, 1625}, {2780, 8552}, {2872, 9142}, {2881, 11641}, {9517, 11615}, {9934, 15478}, {11060, 14398}

= reflection of X(3) in X(6132)

= Gibert circumtangential conjugate of X(10420)

= isogonal conjugate of X(18878)

= X(14687)-of-1st Parry triangle

= X(15919)-of-2nd Parry triangle

= [ 3.7959076033302890, -13.4459239914496000, 11.1974237359893600 ]

 

César Lozada

 

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#4924

 

 Additional note in:

https://amontes.webs.ull.es/otrashtm/HGT2018.htm#HG250818


Angel Montesdeoca