1982 AHSME Problems/Problem 21
Problem
In the adjoining figure, the triangle is a right triangle with
. Median
is perpendicular to median
,
and side
. The length of
is
Solution
Let be the intersection of
and
By the properties of centroids, we have
and
Note that and
are both complementary to
so
By AA, we conclude that
with the ratio of similitude
from which
Applying the Pythagorean Theorem to right
we get
from which
Solving for
gives
~MRENTHUSIASM
See Also
1982 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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