2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4

Revision as of 21:01, 27 September 2019 by Someonenumber011 (talk | contribs) (Solution)


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.


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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)); draw(circle((2,0),1)); dot((-0.5,0.86602)); dot((-0.5,-0.86602)); dot((1,0)); label("$P$",(1,0),NW); [/asy] Where $P$ is the point of tangency. This clearly works, so the smallest distance would be $2*1=\boxed{2}$

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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