ADGEOM 2158 * ADGEOM 2161

#2158

 

Dear geometers,

Let ABC be a triangle with Feuerbach points Fa,Fb,Fc, orthocenter H, circumcircle (O), excircles (Ia),(Ib),(Ic)

Let Fa',Fb',Fc' are symmetric of H through Fa,Fb,Fc we known Fa',Fb',Fc' lie on (O).

Let da be simson line of Fa' wrt triangle ABC. We known that da passes through Fa. So da cuts (Ia) again at point A'. Point B',C' are defined similarly.

Then AA',BB',CC' are concurrent.

Best regards,

Your sincerly,

Tran Quang Hung.

 

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#2161

 

Dear Mr. Hung:

They are concurrent at:

Z = ((b+c)*(a^2-b*c-c^2-b^2)*a)^2/(b+c-a) : :  (barycentrics)

   =  on lines (12,3690), (201,3028), (502,6058)

   = ( 3.942746274236910, 2.62856465180312, 0.001159904088264 )

 

Regards

César Lozada