Proving Euler Line Parallel to Side BC in Triangle ABC

[vaishakh]

Can anyone help me solve the following question. ABC is any triangle. XAB, YBC and ZAC are equilateral triangles formed on this triangle. Prove that AY, BZ and CX are concurrent.


In a triangle ABC, the Euler line is parallel to side BC. Prove that tanB*tanC = 3.

I just need a hint. I don't know how to start with the second problem?

 

[Tx]

For the first, try to proove that Z=X=Y at the orthocentre.
For the second, I have no clue what a Euler line is so I can't help there.

 

[vaishakh]

Euler line is on joning the orthocentre, circumcentre, ninepoint circlecentre and the centroid.