Triangle angles fun

[Jakopos]

There is a triangle XYZ. On XY is a point N, On ZY is a point M. And MY=ZX, XM=XN, XY2=ZY∗XZ a is a angle between ZN and NX, b is a angle between XM and XN Prove that a is equal to b.
I've drawn a picture and tried to do something. I think I need now the information about the ratio beetwen the angles XZN and NZY.

 

[Deleted member 4993]

There is a triangle XYZ. On XY is a point N, On ZY is a point M.
And MY=ZX, XM=XN, XY^2=ZY∗XZ a is a angle between ZN and NX, b is a angle between XM and XN
Prove that a is equal to b
I've drawn a picture and tried to do something. I need now the information what is the ratio betwen the angles XZN and NZY and basically I am stuck at this point.
I would appreciate any help

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[Jakopos]

I am sorry for not reading that post before.
So there are my thoughts:
1. From the equation XY^2=XZ*YZ and from the inequation ZY>=XZ (this one is true because XZ=YM and YMCXZ) I deduced that if XY=a then ZY=xa and ZX=(1/x)a where x∈(1; (5^(1/2)+1)/2)
2.I drew myself this triangle and I tried to add some symetrical triangles etc., and then I tried to count these angles that were possible to count
I am currently in 9th grade but I am doing also individual studying curently.
If you mean functor as in logical sentences f.e. conjunction or alternative then yes I know them.