Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 12"
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== Problem == | == Problem == | ||
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| + | Let <math>ABC</math> be a triangle with <math>AB = 13</math>, <math>BC = 14</math>, and <math>AC = 15</math>. Let <math>D</math> be the foot of the altitude from <math>A</math> to <math>BC</math> and <math>E</math> be the point on <math>BC</math> between <math>D</math> and <math>C</math> such that <math>BD = CE</math>. Extend <math>AE</math> to meet the circumcircle of <math>ABC</math> at <math>F</math>. If the area of triangle <math>FAC</math> is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>m+n</math>. | ||
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| + | == Solution == | ||
== Solution == | == Solution == | ||
Revision as of 21:19, 8 October 2014
Contents
Problem
Let 
be a triangle with 
, 
, and 
. Let 
be the foot of the altitude from 
to 
and 
be the point on between and 
such that 
. Extend 
to meet the circumcircle of at 
. If the area of triangle 
is 
, where 
and 
are relatively prime positive integers, find 
.
Solution
Solution
See also
| Mock AIME 5 2005-2006 (Problems, Source) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
