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Mock AIME 1 2006-2007 Problems/Problem 1: Difference between revisions

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1. <math>\triangle ABC</math> has positive integer side lengths of <math>x</math>,<math>y</math>, and <math>17</math>.  The angle bisector of <math>\angle BAC</math> hits <math>BC</math> at <math>D</math>. If <math>\angle C=90^\circ</math>, and the maximum value of <math>\frac{[ABD]}{[ACD]}=\frac{m}{n}</math> where <math>m</math> and <math>n</math> are relatively prime positive intgers, find <math>m+n</math>. (Note <math>[ABC]</math> denotes the area of <math>\triangle ABC</math>).
<math>\triangle ABC</math> has positive integer side lengths of <math>x</math>,<math>y</math>, and <math>17</math>.  The angle bisector of <math>\angle BAC</math> hits <math>BC</math> at <math>D</math>. If <math>\angle C=90^\circ</math>, and the maximum value of <math>\frac{[ABD]}{[ACD]}=\frac{m}{n}</math> where <math>m</math> and <math>n</math> are relatively prime positive intgers, find <math>m+n</math>. (Note <math>[ABC]</math> denotes the area of <math>\triangle ABC</math>).
 
==Solution==
{{solution}}
 
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[[Mock AIME 1 2006-2007]]
[[Mock AIME 1 2006-2007]]

Revision as of 16:24, 17 August 2006

$\triangle ABC$ has positive integer side lengths of $x$,$y$, and $17$. The angle bisector of $\angle BAC$ hits $BC$ at $D$. If $\angle C=90^\circ$, and the maximum value of $\frac{[ABD]}{[ACD]}=\frac{m}{n}$ where $m$ and $n$ are relatively prime positive intgers, find $m+n$. (Note $[ABC]$ denotes the area of $\triangle ABC$).

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Mock AIME 1 2006-2007

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