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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1999 Moldova Team Selection Test
11
11
Part of
1999 Moldova Team Selection Test
Problems
(1)
is greater than $\frac{2}{3}$ of area of $ABC$
Source: Moldova TST 1999
8/7/2023
Let
A
B
C
ABC
A
BC
be a triangle. Show that there exists a lin
l
l
l
in the plane of
A
B
C
ABC
A
BC
such that the overlapping area of
A
B
C
ABC
A
BC
and
A
′
B
′
C
′
A^{'}B^{'}C^{'}
A
′
B
′
C
′
, the symmetric of
A
B
C
ABC
A
BC
with respect to
l
l
l
, is greater than
2
3
\frac{2}{3}
3
2
of area of
A
B
C
ABC
A
BC
.
geometry