Difference between revisions of "2013 AMC 10A Problems/Problem 25"

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==Problem==
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All 20 diagonals are drawn in a regular octagon. At how many distinct points in the interior
 
All 20 diagonals are drawn in a regular octagon. At how many distinct points in the interior
 
of the octagon (not on the boundary) do two or more diagonals intersect?
 
of the octagon (not on the boundary) do two or more diagonals intersect?
  
 
<math> \textbf{(A)}\ 49\qquad\textbf{(B)}\ 65\qquad\textbf{(C)}\ 70\qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 128 </math>
 
<math> \textbf{(A)}\ 49\qquad\textbf{(B)}\ 65\qquad\textbf{(C)}\ 70\qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 128 </math>
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==Solution==
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==See Also==
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{{AMC10 box|year=2013|ab=A|num-b=24|after=Last Problem}}

Revision as of 22:21, 7 February 2013

Problem

All 20 diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?

$\textbf{(A)}\ 49\qquad\textbf{(B)}\ 65\qquad\textbf{(C)}\ 70\qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 128$

Solution

See Also

2013 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 24
Followed by
Last Problem
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All AMC 10 Problems and Solutions
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