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Problem
Problem
- Let
A
1
,
A
2
,
A
3
,
…
,
A
n
A_1, A_2, A_3, \dots, A_n
A
1
,
A
2
,
A
3
,
…
,
A
n
be the vertices of an
n
n
n
-sided regular polygon such that
1
A
1
A
2
=
1
A
1
A
3
+
1
A
1
A
4
\frac{1}{A_1 A_2} = \frac{1}{A_1 A_3} + \frac{1}{A_1 A_4}
A
1
A
2
1
=
A
1
A
3
1
+
A
1
A
4
1
. Find the value of
n
n
n
. Prove or disprove the converse of this result.
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