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2023 Harvard-MIT Mathematics Tournament
5
weird square( 2023 HMMT G5)
weird square( 2023 HMMT G5)
Source:
February 21, 2023
HMMT
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
13
,
B
C
=
14
,
AB = 13, BC = 14,
A
B
=
13
,
BC
=
14
,
and
C
A
=
15
CA = 15
C
A
=
15
. Suppose
P
Q
R
S
PQRS
PQRS
is a square such that
P
P
P
and
R
R
R
lie on line
B
C
,
Q
BC, Q
BC
,
Q
lies on line
C
A
CA
C
A
, and
S
S
S
lies on line
A
B
AB
A
B
. Compute the side length of this square.
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