# Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 12"

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== Problem == | == Problem == | ||

− | In quadrilateral <math>\displaystyle ABCD,</math> <math>\displaystyle m \angle DAC= m\angle DBC </math> and <math>\displaystyle \ | + | In quadrilateral <math>\displaystyle ABCD,</math> <math>\displaystyle m \angle DAC= m\angle DBC </math> and <math>\displaystyle \frac{[ADB]}{[ABC]}=\frac12.</math> If <math>\displaystyle AD=4,</math> <math>\displaystyle BC=6</math>, <math>\displaystyle BO=1,</math> and the area of <math>\displaystyle ABCD</math> is <math>\displaystyle \frac{a\sqrt{b}}{c},</math> where <math>\displaystyle a,b,c</math> are relatively prime positive integers, find <math>\displaystyle a+b+c.</math> |

+ | Note*: <math>\displaystyle[ABC]</math> and <math>\displaystyle[ADB]</math> refer to the areas of triangles <math>\displaystyle ABC</math> and <math>\displaystyle ADB.</math> | ||

== Problem Source == | == Problem Source == | ||

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

## Revision as of 19:22, 24 July 2006

## Problem

In quadrilateral and If , and the area of is where are relatively prime positive integers, find

Note*: and refer to the areas of triangles and

## Problem Source

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