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A square of side length 2

Source: Vietnam NMO 1989 Problem 3

February 1, 2009

geometrygeometry unsolved

Problem Statement

A square

ABCD

of side length

2

is given on a plane. The segment

AB

is moved continuously towards

CD

until

A

and

C

coincide with

C

and

D

, respectively. Let

S

be the area of the region formed by the segment

AB

while moving. Prove that

AB

can be moved in such a way that

S <\frac{5\pi}{6}

.

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