Difference between revisions of "1985 OIM Problems/Problem 2"
Clarkculus (talk | contribs) (→Solution) |
|||
Line 7: | Line 7: | ||
== Solution == | == Solution == | ||
− | {{ | + | 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 be a point in the interior of equilateral triangle such that: Find the length of one side of the triangle
~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 . It follows that the side length is .