3.5. Znayka cut out a semicircle from paper. Neznaika marked a point $C$ on the diameter $A B$ of this semicircle and cut off two semicircles from Znayka's semicircle with diameters $A C$ and $C B$. The area of the remaining figure turned out to be $10 \pi$. Find the length of the part of the chord lying inside it, passing through point $C$ perpendicular to $A B$. If necessary, round the answer to two decimal places.
Answer: 6.32 (exact value: $2 \sqrt{10}$ ).