2004 AIME II Problem 11

A right circular cone has a base with radius 600 and height 200\sqrt{7}. 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 375\sqrt{2}. Find the least distance that the fly could have crawled.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.