Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 7"

 
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A right circular cone of base radius <math>\displaystyle 17</math>cm and slant height <math>\displaystyle 34</math>cm is given. <math>\displaystyle P</math> is a point on the circumference of the base and the shortest path from <math>\displaystyle P</math> around the cone and back is drawn (see diagram). If the minimum distance from the vertex <math>\displaystyle V</math> to this path is <math>\displaystyle m\sqrt{n},</math> where <math>\displaystyle m</math> and <math>\displaystyle n</math> are relatively prime positive integers, find <math>\displaystyle m+n.</math>
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== Problem ==
  
[[Image:Mock_AIME_2_2007_Problem7.jpg]]
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A right circular cone of base radius <math>\displaystyle 17</math>cm and slant height <math>\displaystyle 34</math>cm is given. <math>\displaystyle P</math> is a point on the circumference of the base and the shortest path from <math>\displaystyle P</math> around the cone and back is drawn (see diagram). If the length of this path is <math>\displaystyle m\sqrt{n},</math> where <math>\displaystyle m</math> and <math>\displaystyle n</math> are relatively prime positive integers, find <math>\displaystyle m+n.</math>
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[[Image:Mock_AIME_2_2007_Problem8.jpg]]

Revision as of 14:09, 25 July 2006

Problem

A right circular cone of base radius $\displaystyle 17$cm and slant height $\displaystyle 34$cm is given. $\displaystyle P$ is a point on the circumference of the base and the shortest path from $\displaystyle P$ around the cone and back is drawn (see diagram). If the length of this path is $\displaystyle m\sqrt{n},$ where $\displaystyle m$ and $\displaystyle n$ are relatively prime positive integers, find $\displaystyle m+n.$

Mock AIME 2 2007 Problem8.jpg

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