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Mock AIME 2 2006-2007 Problems/Problem 12

Revision as of 21:09, 16 February 2007 by Solafidefarms (talk | contribs) (defined O)

Problem

In quadrilateral $\displaystyle ABCD,$ $\displaystyle m \angle DAC= m\angle DBC$ and $\displaystyle \frac{[ADB]}{[ABC]}=\frac12.$ $O$ is defined to be the intersection of the diagonals of $ABCD$. If $\displaystyle AD=4,$ $\displaystyle BC=6$, $\displaystyle BO=1,$ and the area of $\displaystyle ABCD$ is $\displaystyle \frac{a\sqrt{b}}{c},$ where $\displaystyle a,b,c$ are relatively prime positive integers, find $\displaystyle a+b+c.$


Note*: $\displaystyle[ABC]$ and $\displaystyle[ADB]$ refer to the areas of triangles $\displaystyle ABC$ and $\displaystyle ADB.$

Solution

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Problem Source

AoPS users 4everwise and Altheman collaborated to create this problem.

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