3.4. Znayka cut out a semicircle from paper. Neznaika marked a point $D$ on the diameter $A B$ of this semicircle and cut off two semicircles from Znayka's semicircle with diameters $A D$ and $D B$. The area of the remaining figure turned out to be $8 \pi$. Find the length of the part of the chord lying inside it, passing through point $D$ perpendicular to $A B$. If necessary, round the answer to two decimal places.
Answer: 5.66 (exact value: $4 \sqrt{2}$ ).