Minimum distance from the point K
Source: Canada National Mathematical Olympiad 1977 - Problem 5
September 29, 2011
geometry3D geometrygeometry unsolved
Problem Statement
A right circular cone has base radius 1 cm and slant height 3 cm is given. is a point on the circumference of the base and the shortest path from around the cone and back to is drawn (see diagram). What is the minimum distance from the vertex to this path?[asy]
import graph;unitsize(1 cm);filldraw(shift(-0.15,0.37)*rotate(17)*yscale(0.3)*xscale(1.41)*(Circle((0,0),1)),gray(0.9),nullpen);
draw(yscale(0.3)*(arc((0,0),1.5,0,180)),dashed);
draw(yscale(0.3)*(arc((0,0),1.5,180,360)));
draw((1.5,0)--(0,4)--(-1.5,0));
draw((0,0)--(1.5,0),Arrows);
draw(((1.5,0) + (0.3,0.1))--((0,4) + (0.3,0.1)),Arrows);
draw(shift(-0.15,0.37)*rotate(17)*yscale(0.3)*xscale(1.41)*(arc((0,0),1,0,180)),dashed);
draw(shift(-0.15,0.37)*rotate(17)*yscale(0.3)*xscale(1.41)*(arc((0,0),1,180,360)));label("", (0,4), N);
label("1 cm", (0.75,-0.5), N);
label("", (-1.5,0), SW);
label("3 cm", (1.7,2));
[/asy]