Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 9"
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import olympiad; | import olympiad; |
Latest revision as of 23:22, 3 May 2014
Problem
In right triangle
Cevians
and
intersect at
and are drawn to
and
respectively such that
,
and
. If
where
and
are relatively prime and
has no perfect square divisors excluding
find
Solution
Define ,
,
, and
. Note that
implies
.
Let and
be the projections of
onto the legs
and
respectively. Remark that
and
, so
Since
, we have
The requested answer is thus
See Also
Mock AIME 2 2006-2007 (Problems, Source) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |