Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | Let <math>ABC</math> be a triangle such that <math>AB = 68</math>, <math>BC = 100</math>, and <math>CA = 112</math>. Let <math>H</math> be the orthocenter of <math>\triangle ABC</math> (intersection of the altitudes). Let <math>D</math> be the midpoint of <math>BC</math>, <math>E</math> be the midpoint of <math>CA</math>, and <math>F</math> be the midpoint of <math>AB</math>. Points <math>X</math>, <math>Y</math>, and <math>Z</math> are constructed on <math>HD</math>, <math>HE</math>, and <math>HF</math>, respectively, such that <math>D</math> is the midpoint of <math>XH</math>, <math>E</math> is the midpoint of <math>YH</math>, and <math>F</math> is the midpoint of <math>ZH</math>. Find <math>AX+BY+CZ</math>. | ||
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| + | == Solution == | ||
== Solution == | == Solution == | ||
Revision as of 21:20, 8 October 2014
Contents
Problem
Let 
be a triangle such that 
, 
, and 
. Let 
be the orthocenter of 
(intersection of the altitudes). Let 
be the midpoint of 
, 
be the midpoint of 
, and 
be the midpoint of 
. Points 
, 
, and 
are constructed on 
, 
, and 
, respectively, such that is the midpoint of 
, is the midpoint of 
, and is the midpoint of 
. Find 
.
Solution
Solution
See also
| Mock AIME 5 2005-2006 (Problems, Source) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
