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Kvant 2020
M2631
M2631
Part of
Kvant 2020
Problems
(1)
Sides of quadrangle cannot form triangles
Source: 42nd International Tournament of Towns, Junior A-Level P7, Fall 2020
2/18/2023
There is a convex quadrangle
A
B
C
D
ABCD
A
BC
D
such that no three of its sides can form a triangle. Prove that:[*]one of its angles is not greater than
6
0
∘
60^\circ{}
6
0
∘
; [*]one of its angles is at least
12
0
∘
120^\circ
12
0
∘
.Maxim Didin
geometry
Tournament of Towns