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BMT Problems
2021 BMT
17
BMT 2021 Guts Round p17
BMT 2021 Guts Round p17
Source:
October 7, 2022
geometry
Problem Statement
Triangle
△
A
B
C
\vartriangle ABC
△
A
BC
has circumcenter
O
O
O
and orthocenter
H
H
H
. Let
D
D
D
be the foot of the altitude from
A
A
A
to
B
C
BC
BC
, and suppose
A
D
=
12
AD = 12
A
D
=
12
. If
B
D
=
1
4
B
C
BD = \frac14 BC
B
D
=
4
1
BC
and
O
H
∥
B
C
OH \parallel BC
O
H
∥
BC
, compute
A
B
2
AB^2
A
B
2
. .
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