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

(Problem)
Line 1: Line 1:
== '''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?
  
25. All 20 diagonals are drawn in a regular octagon. At how many distinct points in the interior
+
<math> \textbf{(A)}\ 49\qquad\textbf{(B)}\ 65\qquad\textbf{(C)}\ 70\qquad\textbf{(D)}\ 96\qquad\textbf{(E)}\ 128 </math>
of the octagon (not on the boundary) do two or more diagonals intersect?
 
(A) 49  
 
(B) 65  
 
(C) 70  
 
(D) 96  
 
(E) 128
 
  
 +
==Solution==
  
 
70-5-16=49, so THE ANSWER IS A
 
70-5-16=49, so THE ANSWER IS A

Revision as of 00:10, 7 February 2013

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

70-5-16=49, so THE ANSWER IS A

Invalid username
Login to AoPS