Difference between revisions of "1985 OIM Problems/Problem 2"

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== Solution ==
 
== Solution ==
{{solution}}
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By Viviani's Theorem, the altitude of the triangle is the sum of the given lengths, or <math>20</math>. It follows that the side length is <math>\boxed{\frac{40\sqrt3}{3}}</math>.
  
 
== See also ==
 
== See also ==
 
https://www.oma.org.ar/enunciados/ibe1.htm
 
https://www.oma.org.ar/enunciados/ibe1.htm

Latest revision as of 22:36, 8 April 2024

Problem

Let $P$ be a point in the interior of equilateral triangle $ABC$ such that: \[PA=5,\;PB=7,\; and \; PC=8\] Find the length of one side of the triangle $ABC$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

By Viviani's Theorem, the altitude of the triangle is the sum of the given lengths, or $20$. It follows that the side length is $\boxed{\frac{40\sqrt3}{3}}$.

See also

https://www.oma.org.ar/enunciados/ibe1.htm