Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 12"
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Thus <math>[ABCD]=\frac{25\sqrt{143}}{18}\rightarrow\boxed{186}</math> | Thus <math>[ABCD]=\frac{25\sqrt{143}}{18}\rightarrow\boxed{186}</math> | ||
− | ==See | + | ==See Also== |
− | + | {{Mock AIME box|year=2006-2007|n=2|num-b=11|num-a=13}} | |
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== Problem Source == | == Problem Source == | ||
AoPS users 4everwise and Altheman collaborated to create this problem. | AoPS users 4everwise and Altheman collaborated to create this problem. |
Latest revision as of 10:53, 4 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
Mock AIME 2 2006-2007 (Problems, Source) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |
Problem Source
AoPS users 4everwise and Altheman collaborated to create this problem.