If $a, b, c, d$ are continued proportional, then $\dfrac{a}{c} =$

For continued proportion, each common ratio is $r$, so $\frac{a}{c}=r^2$. Substituting $a=cr^2,\,b=cr$ gives $\frac{a^2+b^2}{b^2+c^2}=\frac{c^2r^2(r^2+1)}{c^2(r^2+1)}=r^2$, equal to $\frac{a}{c}$.