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is greater than $\frac{2}{3}$ of area of $ABC$

Source: Moldova TST 1999

August 7, 2023

geometry

Problem Statement

Let

ABC

be a triangle. Show that there exists a lin

l

in the plane of

ABC

such that the overlapping area of

ABC

and

l

, the symmetric of

ABC

with respect to

l

, is greater than

\frac{2}{3}

of area of

ABC

.

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