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Tournament Of Towns
1997 Tournament Of Towns
(532) 4
(532) 4
Part of
1997 Tournament Of Towns
Problems
(1)
[ABC] = 1/2 [AC'BA'C B'$] convex , <A+<B+<C =<A' +<B'+<C'
Source: TOT 532 1997 Spring J A4 - - Tournament Of Towns
9/11/2024
A
C
′
B
A
′
C
B
′
AC' BA'C B'
A
C
′
B
A
′
C
B
′
is a convex hexagon such that
A
B
′
=
A
C
′
AB' = AC'
A
B
′
=
A
C
′
,
B
C
′
=
B
A
′
BC' = BA'
B
C
′
=
B
A
′
,
C
A
′
=
C
B
′
CA' = CB'
C
A
′
=
C
B
′
and
∠
A
+
∠
B
+
∠
C
=
∠
A
′
+
∠
B
′
+
∠
C
′
\angle A +\angle B + \angle C = \angle A' + \angle B' + \angle C'
∠
A
+
∠
B
+
∠
C
=
∠
A
′
+
∠
B
′
+
∠
C
′
. Prove that the area of the triangle
A
B
C
ABC
A
BC
is half the area of the hexagon.(V Proizvolov)
geometry
angles
hexagon
areas