Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 1"
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− | + | <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>). | |
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+ | ==Solution== | ||
+ | {{solution}} | ||
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[[Mock AIME 1 2006-2007]] | [[Mock AIME 1 2006-2007]] |
Revision as of 17:24, 17 August 2006
has positive integer side lengths of
,
, and
. The angle bisector of
hits
at
. If
, and the maximum value of
where
and
are relatively prime positive intgers, find
. (Note
denotes the area of
).
Solution
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