Difference between revisions of "1994 AIME Problems/Problem 15"

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== See also ==
 
== See also ==
 
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{{AIME box|year=1994|num-b=14|after=Last question}}
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[[Category:Intermediate Geometry Problems]]

Revision as of 18:01, 4 December 2007

Problem

Given a point $P^{}_{}$ on a triangular piece of paper $ABC,\,$ consider the creases that are formed in the paper when $A, B,\,$ and $C\,$ are folded onto $P.\,$ Let us call $P_{}^{}$ a fold point of $\triangle ABC\,$ if these creases, which number three unless $P^{}_{}$ is one of the vertices, do not intersect. Suppose that $AB=36, AC=72,\,$ and $\angle B=90^\circ.\,$ Then the area of the set of all fold points of $\triangle ABC\,$ can be written in the form $q\pi-r\sqrt{s},\,$ where $q, r,\,$ and $s\,$ are positive integers and $s\,$ is not divisible by the square of any prime. What is $q+r+s\,$?

Solution

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See also

1994 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Last question
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All AIME Problems and Solutions
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