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University of South Carolina High School Math Contest/1993 Exam/Problem 16

Revision as of 13:16, 23 July 2006 by Joml88 (talk | contribs)

Problem

In the triangle below, $\displaystyle M, N,$ and $P$ are the midpoints of $BC, AB,$ and $AC$ respectively. $CN$ and $AM$ intersect at $O$. If the length of $CQ$ is 4, then what is the length of $OQ$?

Usc93.16.PNG
$\mathrm{(A) \ }1 \qquad \mathrm{(B) \ }4/3 \qquad \mathrm{(C) \ }\sqrt{2} \qquad \mathrm{(D) \ }3/2 \qquad \mathrm{(E) \ }2$

Solution

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