Ex. 104. A regular triangle $ABC$ is inscribed in a circle. Another, smaller circle, is inscribed in the sector bounded by the chord $BC$, touching the larger circle at point $M$, and the chord $BC$ at point $K$. The ray $MK$ intersects the larger circle a second time at point $N$. Find the length of $MN$, if the sum of the distances from point $M$ to the ends of the chord $BC$ is 6.
Ex. 104. 6. Hint. Show that point $N$ coincides with $A$ and use the result of Ex. 28.