Difference between revisions of "2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4"

(Solution)
(Problem)
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Find the smallest and largest possible distances between the centers of two circles of radius
 
Find the smallest and largest possible distances between the centers of two circles of radius
<math>1</math> such that there is an equilateral triangle of side of length <math>1</math> with two vertices on one of
+
<math>1</math> such that there is an equilateral triangle of side length <math>1</math> with two vertices on one of
 
the circles and the third vertex on the second circle.
 
the circles and the third vertex on the second circle.
 
  
 
== Solution ==
 
== Solution ==

Revision as of 20:46, 27 September 2019

Problem

Find the smallest and largest possible distances between the centers of two circles of radius $1$ such that there is an equilateral triangle of side length $1$ with two vertices on one of the circles and the third vertex on the second circle.

Solution

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

The smallest distance would be found if the two circles were externally tangent, so testing that and messing around with it yields [asy] draw(circle((0,0),1));  [/asy]

See also

2014 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions
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