Difference between revisions of "2015 AMC 10B Problems/Problem 12"
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<math>\textbf{(A) }11\qquad \textbf{(B) }12\qquad \textbf{(C) }13\qquad \textbf{(D) }14\qquad \textbf{(E) }15</math> | <math>\textbf{(A) }11\qquad \textbf{(B) }12\qquad \textbf{(C) }13\qquad \textbf{(D) }14\qquad \textbf{(E) }15</math> | ||
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https://youtu.be/RZDFs3qrw7Y | https://youtu.be/RZDFs3qrw7Y | ||
Revision as of 19:41, 25 August 2023
Contents
Problem
For how many integers 
is the point 
inside or on the circle of radius 
centered at 
?
Video Solution
~Education, the Study of Everything=
Solution
The equation of the circle is 
. Plugging in the given conditions we have 
. Expanding gives: 
, which simplifies to
and therefore
and 
. So ranges from 
to 
, for a total of 
integer values.
Note by Williamgolly:
Alternatively, draw out the circle and see that these points must be on the line 
.
See Also
| 2015 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
