Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 12"
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==See also== | ==See also== | ||
− | *[[Mock AIME 2 2006-2007/Problem 11 | Previous Problem]] | + | *[[Mock AIME 2 2006-2007 Problems/Problem 11 | Previous Problem]] |
− | *[[Mock AIME 2 2006-2007/Problem 13 | Next Problem]] | + | *[[Mock AIME 2 2006-2007 Problems/Problem 13 | Next Problem]] |
*[[Mock AIME 2 2006-2007]] | *[[Mock AIME 2 2006-2007]] | ||
Revision as of 15:33, 3 April 2012
Contents
Problem
In quadrilateral
and
is defined to be the intersection of the diagonals of
. If
,
and the area of
is
where
are relatively prime positive integers, find
Note*: and
refer to the areas of triangles
and
Solution
is a cylic quadrilateral.
Let
~
Also, from the Power of a Point Theorem,
Notice
It is given
Note that
Then
and
Thus we need to find
Note that is isosceles with sides
so we can draw the altitude from D to split it to two right triangles.
Thus
See also
Problem Source
AoPS users 4everwise and Altheman collaborated to create this problem.