Difference between revisions of "2012 AIME II Problems/Problem 13"
Williamhu888 (talk | contribs) (Created page with "== Problem 13 == Equilateral <math>\triangle ABC</math> has side length <math>\sqrt{111}</math>. There are four distinct triangles <math>AD_1E_1</math>, <math>AD_1E_2</math>, <ma...") |
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Equilateral <math>\triangle ABC</math> has side length <math>\sqrt{111}</math>. There are four distinct triangles <math>AD_1E_1</math>, <math>AD_1E_2</math>, <math>AD_2E_3</math>, and <math>AD_2E_4</math>, each congruent to <math>\triangle ABC</math>, | Equilateral <math>\triangle ABC</math> has side length <math>\sqrt{111}</math>. There are four distinct triangles <math>AD_1E_1</math>, <math>AD_1E_2</math>, <math>AD_2E_3</math>, and <math>AD_2E_4</math>, each congruent to <math>\triangle ABC</math>, | ||
with <math>BD_1 = BD_2 = \sqrt{11}</math>. Find <math>\sum_{k=1}^4(CE_k)^2</math>. | with <math>BD_1 = BD_2 = \sqrt{11}</math>. Find <math>\sum_{k=1}^4(CE_k)^2</math>. | ||
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| + | == Solution == | ||
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| + | == See also == | ||
| + | {{AIME box|year=2012|n=II|num-b=12|num-a=14}} | ||
Revision as of 16:22, 31 March 2012
Problem 13
Equilateral 
has side length 
. There are four distinct triangles 
, 
, 
, and 
, each congruent to ,
with 
. Find 
.
Solution
See also
| 2012 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
