ADGEOM 4030 * ADGEOM 4031

#4030

Dear Geometers,

Three Euler lines concurrent with angle of them equals to 60 degree

Problem: Let ABC be a triangle, construct on the sides of ABC three equilateral triangles BA'C, CB'A, AC'B either all outward or all inward. Three lines through A', B', C' and parallel to BC, CA, AB form a triangle A''B''C''.

Then show that:

The Euler lines of B'A''C', C'B''A', A'C''B' are concurrent.

The angle of these Euler lines equals to 60 degree.

Which is the point of concurrence in ETC?

Best regards
Sincerely
Dao Thanh Oai

 

 

#4031

 

[Francisco Javier Garcia Capitan]

 

Dear Dao,

 

The point of concurrence are X5617 (equilateral triangles outwards) and X5613 (equilateral triangles inwards).

 

Best regards,

Francisco Javier.