+613 Equilateral triangle ABC is inscribed in a circle. Let M and N be the midpoints of sides ¯AB and ¯AC, respectively. Line MN intersects the circle at P and Q. Compute MB/MC.
+130466 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
