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2020 CMIMC
2020 CMIMC Team
10
2020 Team 10
2020 Team 10
Source:
February 2, 2020
team
2020
Problem Statement
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
?
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