# Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 9"

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

In right triangle <math>\displaystyle ABC,</math> <math>\displaystyle \angle C=90^\circ.</math> Cevians <math>\displaystyle AX</math> and <math>\displaystyle BY</math> intersect at <math>\displaystyle P</math> and are drawn to <math>\displaystyle BC</math> and <math>\displaystyle AC</math> respectively such that <math>\displaystyle \frac{BX}{CX}=\frac23</math> and <math>\displaystyle \frac{AY}{CY}=\sqrt 3.</math> If <math>\displaystyle \tan \angle APB= \frac{a+b\sqrt{c}}{d},</math> where <math>\displaystyle a,b,</math> and <math>\displaystyle d</math> are relatively prime and <math>\displaystyle c</math> has no perfect square divisors excluding <math>\displaystyle 1,</math> find <math>\displaystyle a+b+c+d.</math> | In right triangle <math>\displaystyle ABC,</math> <math>\displaystyle \angle C=90^\circ.</math> Cevians <math>\displaystyle AX</math> and <math>\displaystyle BY</math> intersect at <math>\displaystyle P</math> and are drawn to <math>\displaystyle BC</math> and <math>\displaystyle AC</math> respectively such that <math>\displaystyle \frac{BX}{CX}=\frac23</math> and <math>\displaystyle \frac{AY}{CY}=\sqrt 3.</math> If <math>\displaystyle \tan \angle APB= \frac{a+b\sqrt{c}}{d},</math> where <math>\displaystyle a,b,</math> and <math>\displaystyle d</math> are relatively prime and <math>\displaystyle c</math> has no perfect square divisors excluding <math>\displaystyle 1,</math> find <math>\displaystyle a+b+c+d.</math> | ||

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+ | ==Solution== | ||

+ | {{solution}} | ||

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+ | ---- | ||

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+ | *[[Mock AIME 2 2006-2007/Problem 8 | Previous Problem]] | ||

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+ | *[[Mock AIME 2 2006-2007/Problem 10 | Next Problem]] | ||

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+ | *[[Mock AIME 2 2006-2007]] |

## Revision as of 19:48, 22 August 2006

## Problem

In right triangle Cevians and intersect at and are drawn to and respectively such that and If where and are relatively prime and has no perfect square divisors excluding find

## Solution

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*