MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Stanford Mathematics Tournament
2020 Stanford Mathematics Tournament
7
7
Part of
2020 Stanford Mathematics Tournament
Problems
(1)
SMT 2020 Geometry #7
Source:
8/9/2023
Let
A
B
C
ABC
A
BC
be an acute triangle with
B
C
=
4
BC = 4
BC
=
4
and
A
C
=
5
AC = 5
A
C
=
5
. Let
D
D
D
be the midpoint of
B
C
BC
BC
,
E
E
E
be the foot of the altitude from
B
B
B
to
A
C
AC
A
C
, and
F
F
F
be the intersection of the angle bisector of
∠
B
C
A
\angle BCA
∠
BC
A
with segment
A
B
AB
A
B
. Given that
A
D
AD
A
D
,
B
E
BE
BE
, and
C
F
CF
CF
meet at a single point
P
P
P
, compute the area of triangle
A
B
C
ABC
A
BC
. Express your answer as a common fraction in simplest radical form.
geometry