4.3. Two perpendicular chords $A B$ and $C D$ are drawn in a circle. Determine the distance between the midpoint of segment $A D$ and the line $B C$, if $B D=6, A C=12, B C=10$. Round the answer to two decimal places if necessary.
Answer: 8.47 (exact value: $2 \sqrt{2}+4$ ).