Difference between revisions of "2002 AIME II Problems/Problem 13"
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== See also == | == See also == | ||
{{AIME box|year=2002|n=II|num-b=12|num-a=14}} | {{AIME box|year=2002|n=II|num-b=12|num-a=14}} | ||
+ | {{MAA Notice}} |
Revision as of 20:37, 4 July 2013
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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