ADGEOM 2342 * ADGEOM 2343 * ADGEOM 2344

 #2342

Dear Dr. Paul Yiu, Dr. Kimberling and all Geometers,

Let ABC be a triangle, Let (W) be the circle through X(3),X(110) and X(4240) in ETC.  I found 7 points also lie on (W) as follows:

Let the Euler line of ABC meets the sidelines BC,CA,AB at A0,B0,C0. Six points  X(3), X(110) of three triangles AB0C0, BA0C0, CB0A0 also lie on (W). The circumcenter X(3) of Paralogic triangle whose perpectrix is the Euler line of ABC also lie on (W). So 10 points lie on this circle.

Please see the file attachment.

I am thank to You very much.

Best regards

Sincerely

Dao Thanh Oai

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#2343

Dear Dr. Paul Yiu, Dr. Kimberling and all Geometers,

 

Let O = circumcenter of ABC

Let O'=X(3) of Paralogic triangle whose perpectrix is the Euler line of ABC also lie on (W). So 10 points lie on this circle. OO' be the diameter of this circle

 

Best regards

Sincerely

Dao Thanh Oai

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#2344

Dear Dao Thanh Oai,

The circumcenter of the triangle A1B1C1 is X(5502).

The circle (W) intersects the circumcircle in X(110) and X(1304).

X(4240)=(Euler line of ABC)/\ X(107)X(110) also lie on (W).

Best regards,

Angel Montesdeoca