MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
CMIMC Problems
2020 CMIMC
2020 CMIMC Team
10
10
Part of
2020 CMIMC Team
Problems
(1)
2020 Team 10
Source:
2/2/2020
Let
A
B
C
ABC
A
BC
be a triangle. The incircle
ω
\omega
ω
of
△
A
B
C
\triangle ABC
△
A
BC
, which has radius
3
3
3
, is tangent to
B
C
‾
\overline{BC}
BC
at
D
D
D
. Suppose the length of the altitude from
A
A
A
to
B
C
‾
\overline{BC}
BC
is
15
15
15
and
B
D
2
+
C
D
2
=
33
BD^2 + CD^2 = 33
B
D
2
+
C
D
2
=
33
. What is
B
C
BC
BC
?
team
2020