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2023 Harvard-MIT Mathematics Tournament
8
Stewart (2023 HMMT February Geo #8)
Stewart (2023 HMMT February Geo #8)
Source:
February 20, 2023
HMMT
Problem Statement
Let
△
A
B
C
\triangle ABC
△
A
BC
be a triangle with
∠
B
A
C
>
9
0
∘
\angle BAC>90^{\circ}
∠
B
A
C
>
9
0
∘
,
A
B
=
5
AB=5
A
B
=
5
and
A
C
=
7
AC=7
A
C
=
7
. Points
D
D
D
and
E
E
E
lie on segment
B
C
BC
BC
such that
B
D
=
D
E
=
E
C
BD=DE=EC
B
D
=
D
E
=
EC
. If
∠
B
A
C
+
∠
D
A
E
=
18
0
∘
\angle BAC+\angle DAE=180^{\circ}
∠
B
A
C
+
∠
D
A
E
=
18
0
∘
, compute
B
C
BC
BC
.
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