1968 AHSME Problems/Problem 7

Problem

Let $O$ be the intersection point of medians $AP$ and $CQ$ of triangle $ABC.$ if $OQ$ is 3 inches, then $OP$, in inches, is:

$\text{(A) } 3\quad \text{(B) } \frac{9}{2}\quad \text{(C) } 6\quad \text{(D) } 9\quad \text{(E) } \text{undetermined}$

Solution

The fact that $OQ=3$ only tells us that $CQ=9$. There are infinitely many triangles with a median which has length 9, so we can make no statement about the length of the median $\overline{AP}$ or the segment $\overline{OP}$. Thus, $OP$ is $\fbox{(E) undetermined}$.

See also

1968 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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