2004 AIME II Problems/Problem 11
Problem
A right circular cone has a base with radius 600 and height 
A fly starts at a point on the surface of the cone whose distance from the vertex of the cone is 125, and crawls along the surface of the cone to a point on the exact opposite side of the cone whose distance from the vertex is 
Find the least distance that the fly could have crawled.
Solution
Label the starting point of the fly as 
and the ending as 
and the vertex of the cone as 
.With the give info 
and 
a By Pythagoras the slant height can be calculated by: 
so the slant height of the cone is 800. The base of the cone has a circumference of 
So if we cut the cone along its slant height and through we get a sector of a circle with radius 800. Now the sector is 
. So the sector is 270 degrees. Now we know that and are on opposite sides therefore since lies on a radius of the circle that is the "side" of a 270 degree sector B will lie exactly halfway between so the radius through B will divide the circle into two sectors each with measure 135. Draw in 
to create 
. Now by Law of Cosines 
from there 
