HYACINTHOS 26800

[Antreas P. Hatzipolakis]:

 

[APH]:

 

 

Let ABC be a triangle.

Denote:

Na, Nb, Nc = the NPC centers of IBC, ICA, IAB, resp.

The NPCs of OINa, OINb, OINc are coaxial.

2nd intersection (other then the midpoint of OI) ?

 

 

[César Lozada]:

I2 = 

= 2*a^11-5*(b+c)*a^10+2*(b+2* c)*(2*b+c)*a^9+(b+c)*(2*b^2-9* b*c+2*c^2)*a^8-(3*b^2-5*b*c+3* c^2)*(3*b^2+4*b*c+3*c^2)*a^7+ 9*(b+c)*(b^4+c^4-(b^2-b*c+c^2) *b*c)*a^6-(3*b^6+3*c^6-(3*b^4+ 3*c^4-5*(b^2+c^2)*b*c)*b*c)*a^ 5-(b+c)*(3*b^6+3*c^6-(4*b^4+4* c^4-(8*b^2-15*b*c+8*c^2)*b*c)* b*c)*a^4+(7*b^6+7*c^6-(3*b^4+ 3*c^4-(14*b^2+5*b*c+14*c^2)*b* c)*b*c)*(b-c)^2*a^3-(b^2-c^2)* (b-c)*(4*b^6+4*c^6-(9*b^4+9*c^ 4-2*(7*b^2-6*b*c+7*c^2)*b*c)* b*c)*a^2-(b^2-c^2)^2*(b-c)^2*( b^4+c^4+(b^2+b*c+c^2)*b*c)*a+( b^2-c^2)*(b-c)^2*(b^3+c^3)*(b^ 4-c^4) : : (barys)

= on lines {}

= on the circle centered at X(5901) and passing through X(1125)

= [ 2.488740340039227, 1.37789255701468, 1.538089477802264 ]

 

César Lozada