University of South Carolina High School Math Contest/1993 Exam/Problem 16
Problem
In the triangle below, and
are the midpoints of
and
respectively.
and
intersect at
. If the length of
is 4, then what is the length of
?
![$\mathrm{(A) \ }1 \qquad \mathrm{(B) \ }4/3 \qquad \mathrm{(C) \ }\sqrt{2} \qquad \mathrm{(D) \ }3/2 \qquad \mathrm{(E) \ }2$](http://latex.artofproblemsolving.com/3/b/4/3b4b0d0b2d5665b32ea30490e6d82ef9402ece4e.png)
Solution
and
are the medians of
, so their intersection point
is the centroid of the triangle. Also,
so
is parallel to
and thus
and
. Then
. Since the centroid trisects the medians,
and
which is answer choice
.