4

Part of 1983 Swedish Mathematical Competition

Problems(1)

rectangle with max area and sides on 2 concentric circles

Source: 1983 Swedish Mathematical Competition p4

C

C'

are concentric circles with radii

R

R'

. A rectangle has two adjacent vertices on

C

and the other two vertices on

C'

. Find its sides if its area is as large as possible.

geometryrectangleconcentricmaxtriangle areatriangle inequality