# Know the degree of the equation with the radicals expanded

I have an equation with radicals. I would like to know what would be the degree of the polynomials if I'd move the terms and square the equation a number of times sufficient to remove all the radicals.

How could I achieve this in Mathematica?

Practically, in the following equation nu12==0 I would like to know the degree of t once all the radicals are removed

C1 := c1*Cos[phi + xi1] - b*Cos[psi1] - ox1
D1 := c1*Sin[phi + xi1] - b*Sin[psi1] - oy1
oneToTwo := {c1 -> c2, xi1 -> xi2, psi1 -> psi2, ox1 -> ox2, oy1 -> oy2}
C2 := C1 /. oneToTwo
D2 := D1 /. oneToTwo
hcd = (C2^2 - C1^2 - D1^2 + D2^2)/(2*(D1 - D2))
numcd = TrigExpand[
Numerator[Together[Simplify[C1^2 + (hcd + D1)^2 - a^2]]]]
cogamma = c2*Sin[psi1]*Cos[phi + xi2] - c1*Sin[psi1 - phi - xi1]
sigamma = c2*Sin[phi + xi2]*Sin[psi1]
Weier := {Sin[phi] -> (2 t)/(1 + t^2), Cos[phi] -> (1 - t^2)/(1 + t^2)}
nu12 = TrigExpand[Numerator[Together[
numcd /. {Sin[psi2] -> sigamma/Sqrt[sigamma^2 + cogamma^2],
Cos[psi2] -> cogamma/Sqrt[sigamma^2 + cogamma^2]}]]] /. Weier