ADGEOM 3881 * ADGEOM 3884

#3881

 

Dear geometers,

 

Let S be the symmedian point ò ABC.

 

S' is isotomic conjugate of S wrt ABC.

 

A'B'C' is cevian triangle of S' wrt ABC.

 

S* is isogonal conjugate of S wrt A'B'C'.

 

Then S* lies on Euler line of ABC. 

 

Which is this point ?

 

Best regards,

Tran Quang Hung.

 

 

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#3884

 

The first barycentric coordinate of  the point S* on Euler line is

a^12-a^8 (b^4+b^2 c^2+c^4)+2 a^6 (b^6+c^6)+a^4 (b^8+b^6 c^2-2 b^4 c^4+b^2 c^6+c^8)-2 a^2 (b^10+b^6 c^4+b^4 c^6+c^10)-(b^4-c^4)^2 (b^4+c^4)

 (6 - 9 - 13) - search numbers (5.07596651974519, 4.19305606900199, -1.60497426728401).
 
 Angel Montesdeoca