Mock AIME 2 2006-2007 Problems/Problem 12
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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.