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Montgomery Blair
MBMT Team Rounds
2020.42
2020.42
Part of
MBMT Team Rounds
Problems
(1)
integer lenght of angle bisector 2020 MBMT p42
Source:
2/13/2022
△
A
B
C
\vartriangle ABC
△
A
BC
has side lengths
A
B
=
4
AB = 4
A
B
=
4
and
A
C
=
9
AC = 9
A
C
=
9
. Angle bisector
A
D
AD
A
D
bisects angle
A
A
A
and intersects
B
C
BC
BC
at
D
D
D
. Let
k
k
k
be the ratio
B
D
A
B
\frac{BD}{AB}
A
B
B
D
. Given that the length
A
D
AD
A
D
is an integer, find the sum of all possible
k
2
k^2
k
2
.
geometry
angle bisector
MBMT