Difference between revisions of "2004 AMC 12B Problems/Problem 24"
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| − | + | == Problem == | |
| + | In <math>\triangle ABC</math>, <math>AB = BC</math>, and <math>\overline{BD}</math> is an [[altitude]]. Point <math>E</math> is on the extension of <math>\overline{AC}</math> such that <math>BE = 10</math>. The values of <math>\tan \angle CBE</math>, <math>\tan \angle DBE</math>, and <math>\tan \angle ABE</math> form a [[geometric progression]], and the values of <math>\cot \angle DBE, \cot \angle CBE, \cot \angle DBC</math> form an [[arithmetic progression]]. What is the area of <math>\triangle ABC</math>? | ||
| + | |||
| + | <math>\mathrm{(A)}\ 16 | ||
| + | \qquad\mathrm{(B)}\ \frac {50}3 | ||
| + | \qquad\mathrm{(C)}\ 10\sqrt{3} | ||
| + | \qquad\mathrm{(D)}\ 8\sqrt{5} | ||
| + | \qquad\mathrm{(E)}\ 18</math> | ||
| + | == Solution == | ||
| + | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | {{AMC12 box|year=2004|ab=B|num-b=23|num-a=25}} | ||
| + | |||
| + | [[Category:Intermediate Geometry Problems]] | ||
| + | [[Category:Intermediate Trigonometry Problems]] | ||
Revision as of 11:11, 10 February 2008
Problem
In 
, 
, and 
is an altitude. Point 
is on the extension of 
such that 
. The values of 
, 
, and 
form a geometric progression, and the values of 
form an arithmetic progression. What is the area of ?
Solution
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See also
| 2004 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by Problem 25 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
