+585 Equilateral triangle ABC is inscribed in a circle. Let $M$ and $N$ be the midpoints of sides $\overline{AB}$ and $\overline{AC},$ respectively. Line $MN$ intersects the circle at $P$ and $Q.$ Compute MB/MC.
+130081 Let the circle have a radius of 4
Let A = (0,4)
Let B = ( 2sqrt 3 , -2 )
AB = sqrt [ (2sqrt 3)^2 + (4--2)^2] = sqrt 48 = 4sqrt (3) side length of triangle
MC = = (1/2) side length = 2sqrt 3
MB = side length * sqrt 3 = 2 sqrt 3 * sqrt 3 = 6
MB /MC = 6 / [ 2sqrt 3] = 3 /sqrt 3 = sqrt 3
