Difference between revisions of "2017 AMC 10A Problems/Problem 17"

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==Problem==
 
==Problem==
 
Distinct points <math>P</math>, <math>Q</math>, <math>R</math>, <math>S</math> lie on the circle <math>x^2+y^2=25</math> and have integer coordinates. The distances <math>PQ</math> and <math>RS</math>  are irrational numbers. What is the greatest possible value of the ratio <math>\frac{PQ}{RS}</math>?
 
Distinct points <math>P</math>, <math>Q</math>, <math>R</math>, <math>S</math> lie on the circle <math>x^2+y^2=25</math> and have integer coordinates. The distances <math>PQ</math> and <math>RS</math>  are irrational numbers. What is the greatest possible value of the ratio <math>\frac{PQ}{RS}</math>?
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<math>\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 5\qquad\mathrm{(C)}\ 3\sqrt{5}\qquad\mathrm{(D)}\ 7\qquad\mathrm{(E)}\ 5\sqrt{2}</math>
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2017|ab=A|num-b=16|num-a=18}}
 
{{AMC10 box|year=2017|ab=A|num-b=16|num-a=18}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 18:10, 8 February 2017

Problem

Distinct points $P$, $Q$, $R$, $S$ lie on the circle $x^2+y^2=25$ and have integer coordinates. The distances $PQ$ and $RS$ are irrational numbers. What is the greatest possible value of the ratio $\frac{PQ}{RS}$?

$\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 5\qquad\mathrm{(C)}\ 3\sqrt{5}\qquad\mathrm{(D)}\ 7\qquad\mathrm{(E)}\ 5\sqrt{2}$

See Also

2017 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 16
Followed by
Problem 18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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