1983 AHSME Problems/Problem 19
Problem
Point is on side
of triangle
. If
,
then the length of
is
Solution
Let . Since
bisects
, the Angle Bisector Theorem gives
, so write
and
. Applying the Law of Cosines to
gives
, and to
gives
. Subtracting
times the first equation from the second equation therefore yields
, so
is
or
. But since
(
is the length of a side of a triangle),
must be
, so the answer is
.