3

Part of 1985 Canada National Olympiad

Problems(1)

Sum of the perimeters is at least twice the circumference

Source:

P_1

P_2

be regular polygons of 1985 sides and perimeters

x

y

respectively. Each side of

P_1

is tangent to a given circle of circumference

c

and this circle passes through each vertex of

P_2

x + y \ge 2c

. (You may assume that

\tan \theta \ge \theta

0 \le \theta < \frac{\pi}{2}

geometryperimetertrigonometrycalculusintegrationinequalities