Seeing diagram solves the problem

Let the angles subtended by sides of length $\sqrt2$ and $\sqrt{24}$ at the centre be $\alpha$ and $\beta$ respectively. Then, $6(\alpha+\beta)=2\pi \Rightarrow\alpha+\beta=\frac{\pi}{3}$ $2R\sin{\frac{\alpha}{2}}=\sqrt2$ $2R\sin{\frac{\beta}{2}}=\sqrt{24}$

Now, bashing gives the result $R=\sqrt{38}$ .

What was the intended solution?