2004 AMC 12B Problems/Problem 24
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
Let . Then the first condition tells us that and multiplying out gives us . Since , we have .
The second condition tells us that . Expanding, we have . Evidently , so we get .
Now and . Thus, .
See also
2004 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
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All AMC 12 Problems and Solutions |
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