Difference between revisions of "1953 AHSME Problems/Problem 14"

(Created page with "==Problem 14== Given the larger of two circles with center <math>P</math> and radius <math>p</math> and the smaller with center <math>Q</math> and radius <math>q</math>. Draw...")
 
(Problem 14)
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Given the larger of two circles with center <math>P</math> and radius <math>p</math> and the smaller with center <math>Q</math> and radius <math>q</math>. Draw <math>PQ</math>. Which of the following statements is false?  
 
Given the larger of two circles with center <math>P</math> and radius <math>p</math> and the smaller with center <math>Q</math> and radius <math>q</math>. Draw <math>PQ</math>. Which of the following statements is false?  
  
$\textbf{(A)}\ p-q\text{ can be equal to }\overline{PQ}\  
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<math>\textbf{(A)}\ p-q\text{ can be equal to }\overline{PQ}\  
 
\textbf{(B)}\ p+q\text{ can be equal to }\overline{PQ}\  
 
\textbf{(B)}\ p+q\text{ can be equal to }\overline{PQ}\  
 
\textbf{(C)}\ p+q\text{ can be less than }\overline{PQ}\  
 
\textbf{(C)}\ p+q\text{ can be less than }\overline{PQ}\  
\textbf{(D)}\ p-q\text{ can be less than }\overline{PQ}\ \textbf{(E)}\ \text{none of these}
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\textbf{(D)}\ p-q\text{ can be less than }\overline{PQ}\ \textbf{(E)}\ \text{none of these} </math>

Revision as of 14:26, 15 July 2018

Problem 14

Given the larger of two circles with center $P$ and radius $p$ and the smaller with center $Q$ and radius $q$. Draw $PQ$. Which of the following statements is false?

$\textbf{(A)}\ p-q\text{ can be equal to }\overline{PQ}\\  \textbf{(B)}\ p+q\text{ can be equal to }\overline{PQ}\\  \textbf{(C)}\ p+q\text{ can be less than }\overline{PQ}\\  \textbf{(D)}\ p-q\text{ can be less than }\overline{PQ}\\ \textbf{(E)}\ \text{none of these}$