2005.1

Part of Indonesia Regional MO OSP SMA - geometry

Problems(1)

min of max sidelength of an inscribed quadrilateral in circle of radius 1

Source: 2005 Indonedia MO Province P2 q1

The length of the largest side of the cyclic quadrilateral

ABCD

a

, while the radius of the circumcircle of

\vartriangle ACD

1

. Find the smallest possible value for

a

. Which cyclic quadrilateral

ABCD

gives the value

a

equal to the smallest value?

geometrycyclic quadrilateralgeometric inequality