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1972 All Soviet Union Mathematical Olympiad
167
ASU 167 All Soviet Union MO 1972 angles in inscribed heptagon
ASU 167 All Soviet Union MO 1972 angles in inscribed heptagon
Source:
July 3, 2019
geometry
Heptagon
Cyclic
Problem Statement
The
7
7
7
-gon
A
1
A
2
A
3
A
4
A
5
A
6
A
7
A_1A_2A_3A_4A_5A_6A_7
A
1
A
2
A
3
A
4
A
5
A
6
A
7
is inscribed in a circle. Prove that if the centre of the circle is inside the
7
7
7
-gon , than
∠
A
1
+
∠
A
2
+
∠
A
3
<
45
0
o
\angle A_1+ \angle A_2 + \angle A_3 < 450^o
∠
A
1
+
∠
A
2
+
∠
A
3
<
45
0
o
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