# Difference between revisions of "1995 AIME Problems/Problem 9"

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

+ | Triangle <math>\displaystyle ABC</math> is isosceles, with <math>\displaystyle AB=AC</math> and altitude <math>\displaystyle AM=11.</math> Suppose that there is a point <math>\displaystyle D</math> on <math>\displaystyle \overline{AM}</math> with <math>\displaystyle AD=10</math> and <math>\displaystyle \angle BDC=3\angle BAC.</math> Then the perimeter of <math>\displaystyle \triangle ABC</math> may be written in the form <math>\displaystyle a+\sqrt{b},</math> where <math>\displaystyle a</math> and <math>\displaystyle b</math> are integers. Find <math>\displaystyle a+b.</math> | ||

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+ | [[Image:AIME_1995_Problem_9.png]] | ||

== Solution == | == Solution == | ||

== See also == | == See also == | ||

+ | * [[1995_AIME_Problems/Problem_8|Previous Problem]] | ||

+ | * [[1995_AIME_Problems/Problem_10|Next Problem]] | ||

* [[1995 AIME Problems]] | * [[1995 AIME Problems]] |

## Revision as of 01:21, 22 January 2007

## Problem

Triangle is isosceles, with and altitude Suppose that there is a point on with and Then the perimeter of may be written in the form where and are integers. Find