1

Part of 2005 Cuba MO

Problems(2)

5 unit circles in a square, min square side

Source: 2005 Cuba MO 1.1

Determine the smallest real number

a

such that there is a square of side

a

such that contains

5

unit circles inside it without common interior points in pairs.

geometrycirclesgeometric inequality

2 triangles of equal perimeter and area 2005 Cuba MO 2.1

Source:

Determine all the quadrilaterals that can be divided by a diagonal into two triangles of equal area and equal perimeter.

geometryperimeterequal areas