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Eotvos Mathematical Competition (Hungary)
1899 Eotvos Mathematical Competition
1
1
Part of
1899 Eotvos Mathematical Competition
Problems
(1)
The points $A_0, A_1, A_2, A_3, A_4$ divide a unit circle (circle of radius $1$)
Source: Eotvos 1899 p1
3/14/2020
The points
A
0
,
A
1
,
A
2
,
A
3
,
A
4
A_0, A_1, A_2, A_3, A_4
A
0
,
A
1
,
A
2
,
A
3
,
A
4
divide a unit circle (circle of radius
1
1
1
) into five equal parts. Prove that the chords
A
0
,
A
1
,
A
0
,
A
2
A_0, A_1, A_0, A_2
A
0
,
A
1
,
A
0
,
A
2
satisfy
(
A
0
A
1
⋅
A
0
A
2
)
2
=
5
(A_0A_1 \cdot A_0A_2)^2= 5
(
A
0
A
1
⋅
A
0
A
2
)
2
=
5
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