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Putnam
1955 Putnam
A2
Putnam 1955 A2
Putnam 1955 A2
Source:
May 23, 2022
Putnam
Problem Statement
A
1
A
2
…
A
n
A_1 ~A_2~ \ldots ~A_n
A
1
A
2
…
A
n
is a regular polygon inscribed in a circle of radius
r
r
r
and center
O
.
O.
O
.
P
P
P
is a point on line
O
A
1
OA_1
O
A
1
extended beyond
A
1
.
A_1.
A
1
.
Show that
∏
i
=
1
n
P
A
‾
i
=
O
P
‾
n
−
r
n
.
\prod^n_{i=1} ~ \overline{PA}_{~i} = \overline{OP}^{~n} - r^n.
i
=
1
∏
n
P
A
i
=
OP
n
−
r
n
.
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