Difference between revisions of "2014 AIME I Problems/Problem 15"
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== Problem 15 == | == Problem 15 == | ||
| − | In \triangle ABC, AB = 3, BC = 4, and CA = 5. Circle \omega intersects \overline{AB} at E and B, \overline{BC} at B and D, and \overline{AC} at F and G. Given that EF=DF and \frac{DG}{EG} = \frac{3}{4}, | + | In <math>\triangle ABC</math>, <math>AB = 3</math>, <math>BC = 4</math>, and <math>CA = 5</math>. Circle <math>\omega</math> intersects <math>\overline{AB}</math> at <math>E</math> and <math>B</math>, <math>\overline{BC}</math> at <math>B</math> and <math>D</math>, and <math>\overline{AC}</math> at <math>F</math> and <math>G</math>. Given that <math>EF=DF</math> and <math>\frac{DG}{EG} = \frac{3}{4}</math>, <math>DE=\frac{a\sqrt{b}}{c}</math>, where <math>a</math> and <math>c</math> are relatively prime positive integers, and <math>b</math> is a positive integer not divisible by the square of any prime. Find <math>a+b+c</math>. |
== Solution == | == Solution == | ||
Revision as of 17:19, 14 March 2014
Problem 15
In 
, 
, 
, and 
. Circle 
intersects 
at 
and 
, 
at and 
, and 
at 
and 
. Given that 
and 
, 
, where 
and 
are relatively prime positive integers, and 
is a positive integer not divisible by the square of any prime. Find 
.
