Ex. 103. A diameter divides a circle into two parts, one of which contains a smaller inscribed circle touching the larger circle at point $M$, and the diameter at point $K$. The ray $MK$ intersects the larger circle a second time at point 

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$N$. Find the length of $MN$, if the sum of the distances from point $M$ to the ends of the diameter is 6.
Ex.103. $3 \sqrt{2}$. Hint. Show that point $N$ is the midpoint of the second semicircle and use the generalized sine theorem to calculate $M N$.