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International Contests
Tournament Of Towns
1996 Tournament Of Towns
(493) 6
(493) 6
Part of
1996 Tournament Of Towns
Problems
(1)
sum of n - 1 angles is 30^o, n equal parts of side of equilateral
Source: TOT 493 1996 Spring J A6 Tournament Of Towns
8/16/2024
In an equilateral triangle
A
B
C
ABC
A
BC
, let
D
D
D
be a point on the side
A
B
AB
A
B
such that
A
D
=
A
B
/
n
AD = AB /n
A
D
=
A
B
/
n
. Prove that the sum of
n
−
1
n - 1
n
−
1
angles
∠
D
P
l
A
\angle DP_lA
∠
D
P
l
A
,
∠
D
P
2
A
\angle DP_2A
∠
D
P
2
A
,
.
.
.
...
...
,
∠
D
P
n
A
\angle DP_nA
∠
D
P
n
A
where
P
1
P_1
P
1
,
P
2
P_2
P
2
,
.
.
.
...
...
,
P
n
−
1
P_{n-1}
P
n
−
1
are the points dividing the side
B
C
BC
BC
into
n
n
n
equal parts, is equal to
30
30
30
degrees if(a)
n
=
3
n = 3
n
=
3
(b)
n
n
n
is an arbitrary integer,
n
>
2
n > 2
n
>
2
. (V Proizvolov)
geometry
angles