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Difference between revisions of "2005 AIME II Problems/Problem 10"

 
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== Problem ==
 
== Problem ==
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Triangle <math>ABC</math> lies in the Cartesian Plane and has an area of 70. The coordinates of <math>B</math> and <math>C</math> are <math>(12,19)</math> and <math>(23,20),</math> respectively, and the coordinates of <math>A</math> are <math>(p,q).</math> The line containing the median to side <math>BC</math> has slope <math>-5</math>. Find the largest possible value of <math>p+q</math>.
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Given that <math> O </math> is a regular octahedron, that <math> C </math> is the cube whose vertices are the centers of the faces of <math> O, </math> and that the ratio of the volume of <math> O </math> to that of <math> C </math> is <math> \frac mn, </math> where <math> m </math> and <math> n </math> are relatively prime integers, find <math> m+n. </math>
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== Solution ==
 
== Solution ==
 
== See Also ==
 
== See Also ==
 
*[[2005 AIME II Problems]]
 
*[[2005 AIME II Problems]]

Revision as of 22:28, 8 July 2006

Problem

Given that $O$ is a regular octahedron, that $C$ is the cube whose vertices are the centers of the faces of $O,$ and that the ratio of the volume of $O$ to that of $C$ is $\frac mn,$ where $m$ and $n$ are relatively prime integers, find $m+n.$

Solution

See Also

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