MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2016 Harvard-MIT Mathematics Tournament
14
14
Part of
2016 Harvard-MIT Mathematics Tournament
Problems
(1)
2016 Guts #14
Source:
12/24/2016
Let
A
B
C
ABC
A
BC
be a triangle such that
A
B
=
13
AB = 13
A
B
=
13
,
B
C
=
14
BC = 14
BC
=
14
,
C
A
=
15
CA = 15
C
A
=
15
and let
E
E
E
,
F
F
F
be the feet of the altitudes from
B
B
B
and
C
C
C
, respectively. Let the circumcircle of triangle
A
E
F
AEF
A
EF
be
ω
\omega
ω
. We draw three lines, tangent to the circumcircle of triangle
A
E
F
AEF
A
EF
at
A
A
A
,
E
E
E
, and
F
F
F
. Compute the area of the triangle these three lines determine.