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17
Math Prize 2021 Problem 17
Math Prize 2021 Problem 17
Source:
September 19, 2021
Math Prize for Girls
Problem Statement
In the coordinate plane, let
A
=
(
−
8
,
0
)
A = (-8, 0)
A
=
(
−
8
,
0
)
,
B
=
(
8
,
0
)
B = (8, 0)
B
=
(
8
,
0
)
, and
C
=
(
t
,
6
)
C = (t, 6)
C
=
(
t
,
6
)
. What is the maximum value of
sin
m
∠
C
A
B
⋅
sin
m
∠
C
B
A
\sin m\angle CAB \cdot \sin m\angle CBA
sin
m
∠
C
A
B
⋅
sin
m
∠
CB
A
, over all real numbers
t
t
t
?
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