correlation coefficient bivariate normally distributed

Suppose that X,Y and X,Z are bivariate normally distributed. We have

$$E(X)=0, Var(X)=10$$, $$E(Y)=0, Var(Y)=6$$ and $$ρ_{xy}=0.87$$

Moreover,

$$E(X)=0, Var(X)=10$$, $$E(Z)=0, Var(Z)=4$$ and $$ρ_{xz}=0.87$$

Indicating as K the joint distribution of Y and Z,i know from the theory of the problem i'm dealing with that K is for sure a bivariate normally distributed. I expect this will pose some constraint on the value of $$ρ_{yz}$$