Difference between revisions of "1994 AIME Problems/Problem 15"
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== Problem == | == Problem == | ||
| + | Given a point <math>P^{}_{}</math> on a triangular piece of paper <math>ABC,\,</math> consider the creases that are formed in the paper when <math>A, B,\,</math> and <math>C\,</math> are folded onto <math>P.\,</math> Let us call <math>P_{}^{}</math> a fold point of <math>\triangle ABC\,</math> if these creases, which number three unless <math>P^{}_{}</math> is one of the vertices, do not intersect. Suppose that <math>AB=36, AC=72,\,</math> and <math>\angle B=90^\circ.\,</math> Then the area of the set of all fold points of <math>\triangle ABC\,</math> can be written in the form <math>q\pi-r\sqrt{s},\,</math> where <math>q, r,\,</math> and <math>s\,</math> are positive integers and <math>s\,</math> is not divisible by the square of any prime. What is <math>q+r+s\,</math>? | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
| − | + | {{AIME box|year=1994|num-b=14|after=Last question}} | |
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Revision as of 22:47, 28 March 2007
Problem
Given a point 
on a triangular piece of paper 
consider the creases that are formed in the paper when 
and 
are folded onto 
Let us call 
a fold point of 
if these creases, which number three unless is one of the vertices, do not intersect. Suppose that 
and 
Then the area of the set of all fold points of can be written in the form 
where 
and 
are positive integers and is not divisible by the square of any prime. What is 
?
Solution
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See also
| 1994 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
