4.2. Quadrilateral $K L M N$ with sides $K L=4, L M=10, M N=12$ is inscribed in a circle. Determine the distance between the midpoint of side $K N$ and the line $L M$, if the lines $K M$ and $L N$ are perpendicular. Round your answer to two decimal places if necessary.
Answer: 6.87 (exact value: $\sqrt{15}+3$ ).