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Difference between revisions of "2019 CIME I Problems/Problem 14"

(Created page with "Let <math>ABC</math> be a triangle with circumcenter <math>O</math> and incenter <math>I</math> such that the lengths of the three segments <math>AB</math>, <math>BC</math>, a...")
 
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Let <math>ABC</math> be a triangle with circumcenter <math>O</math> and incenter <math>I</math> such that the lengths of the three segments <math>AB</math>, <math>BC</math>, and <math>CA</math> form an increasing arithmetic progression in this order. If <math>AO=60</math> and <math>AI=58</math>, then the distance from <math>A</math> to <math>BC</math> can be expressed as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.
 
Let <math>ABC</math> be a triangle with circumcenter <math>O</math> and incenter <math>I</math> such that the lengths of the three segments <math>AB</math>, <math>BC</math>, and <math>CA</math> form an increasing arithmetic progression in this order. If <math>AO=60</math> and <math>AI=58</math>, then the distance from <math>A</math> to <math>BC</math> can be expressed as <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.
  
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{{CIME box|year=2019|n=I|num-b=13|num-a=15}}
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[[Category:Intermediate Geometry Problems]]
 
{{MAC Notice}}
 
{{MAC Notice}}

Revision as of 16:04, 3 October 2020

Let $ABC$ be a triangle with circumcenter $O$ and incenter $I$ such that the lengths of the three segments $AB$, $BC$, and $CA$ form an increasing arithmetic progression in this order. If $AO=60$ and $AI=58$, then the distance from $A$ to $BC$ can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

2019 CIME I (Problems • Answer Key • Resources)
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Problem 13 		Followed by
Problem 15
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