ADGEOM 2511 * ADGEOM 2512 * ADGEOM 2513

 

#2511

 

I have seen problem

Three radical axis of three pair mixtilinear incircle and mixtilinear excircle at each vertex bound a triangle that its circumcircle is tangent to circumcircle of reference triangle.

Best regards,

Your sincerly,

Tran Quang Hung.

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#2512

Dear geometers,

Sorry because my mistake, I fixed problem as

Three radical axis of three pair mixtilinear incircle and mixtilinear excircle at each vertex bound a triangle that its incircle is tangent to circumcircle of reference triangle.

Best regards,
Your sincerly,
Tran Quang Hung.

 

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#2513

Dear Dear Tran Quang Hung,

This triangle is the hexyl triangle, and its incircle touches the circumcircle at a point P surprisingly not in ETC.  It is equivalently:

X(119) of excentral triangle
X(11) of hexyl triangle
X(100) of 2nd circumperp triangle
circumcircle antipode of X(3659)
Λ(X(1), X(167))
Λ(X(10), X(2090))
Λ(X(40), X(164))
Λ(X(178), X(946))
On lines (3,164) (109,260) (at least)

ETC search:12.038083598321457

Best regards,
Randy Hutson