Difference between revisions of "Mock AIME 1 Pre 2005 Problems/Problem 15"
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== Problem == | == Problem == | ||
| − | + | Triangle <math>ABC</math> has an inradius of <math>5</math> and a circumradius of <math>16</math>. If <math>2\cos{B} = \cos{A} + \cos{C}</math>, then the area of triangle <math>ABC</math> can be expressed as <math>\frac{a\sqrt{b}}{c}</math>, where <math>a, b,</math> and <math>c</math> are positive integers such that <math>a</math> and <math>c</math> are relatively prime and <math>b</math> is not divisible by the square of any prime. Compute <math>a+b+c</math>. | |
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== Solution == | == Solution == | ||
Revision as of 16:28, 8 October 2014
Problem
Triangle 
has an inradius of 
and a circumradius of 
. If 
, then the area of triangle can be expressed as 
, where 
and 
are positive integers such that 
and are relatively prime and 
is not divisible by the square of any prime. Compute 
.
Solution
See also
| Mock AIME 1 Pre 2005 (Problems, Source) | ||
| Preceded by Problem 14 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
