On the binormal of a space curve of constant torsion $\tau$, a point $Q$ is taken at a constant distance $c$ from the curve. Show that the binormal to the locus of $Q$ is inclined to the binormal of the given curve at an angle $\tan^{-1}\left(\frac{c\tau^2}{k\sqrt{c^2\tau^2+1}}\right)$
Suppose that a point $Q$ is taken on the binormal of the curve at a constant distance $c$ from the curve. Let, $y(s_1)=\vec{OQ}$ represents the locus of $Q$ on the binormal of $c$. $\vec{OQ}=\vec{OP}+\vec{PQ}$ or $\underline{y}=\underline{x}+c\underline{b}$. Differentiate with respect to $s$,
$$ \begin{align} \frac{d\underline{y}}{ds_1}\frac{ds_1}{ds}&=\underline{x'}+c\underline{b'}\\ t_1\frac{ds_1}{ds}&=t-c\tau n\\ \left(\frac{ds_1}{ds}\right)^2&=1+c^2\tau^2\\ \frac{ds_1}{ds}&=\sqrt{1+c^2\tau^2} \end{align} $$
From here, I couldn't manage to think further. Any help would be appreciated.
I didn't understand how to approach this kind of problem. If anyone has any book suggestion, then let me know.
Thanks in advance.