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 $\fbox{(E) undetermined}$ .

1968 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1968 AHSME Problems/Problem 7

Problem

Solution

See also