2002 AIME II Problems/Problem 13
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Problem
In triangle point is on with and point is on with and and and intersect at Points and lie on so that is parallel to and is parallel to It is given that the ratio of the area of triangle to the area of triangle is where and are relatively prime positive integers. Find .
Solution
Let be the intersection of and .
Since and , and . So , and thus, .
Using mass points:
WLOG, let .
Then:
.
.
.
.
Thus, . Therefore, , and .
See also
2002 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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