We can use Pythagoras' rule to find the length of AC.
The length of CB1 is less easy to find, but we could, for example, use a method like the one we used for BA1 involving similar triangles. Here, a useful triangle is the 1 by 3 right-angled triangle with a vertext at C and whose hypotenuse (of length √10) lies on CB1 produced.
the end

a high-res pdf file of this new GEOaa-zz task