HYACINTHOS 28859

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle with (Ia), (Ib), (Ic) the three excircles.

 

Denote:

(I1), (I2), (I3) = the reflections of  (Ia), (Ib), (Ic) in IbIc, IcIa, IaIb, resp.

A* = the radical center of (I1), (Ib), (Ic)

B* = the radical center of (Ia), (I2), (Ic)  

C* = the radical center of (Ia), (Ib), (I3)    

ABC, A*B*C* are perspective.

 

 

[Peter Moses]:

Hi Antreas,

At X(58).

Also, perspective to the Caelum triangle (see X(5603)) at W = 

 

= X(1)X(4015)∩X(106)X(5297)

 

= a*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3 + 3*a^2*c + a*b*c + 8*b^2*c + 4*a*c^2 + 8*b*c^2 + 2*c^3) : : 

 

= lies on these lines: {1, 4015}, {106, 5297}, {519, 25354}, {551, 3699}, {1022, 1390}, {3242, 4260}, {3722, 4653}, {4669, 17600}, {4752, 16521}

 

Best regards,
Peter Moses.