MathDB

Sum of the perimeters is at least twice the circumference

Source:

September 30, 2011

geometryperimetertrigonometrycalculusintegrationinequalities

Problem Statement

Let

P_1

and

P_2

be regular polygons of 1985 sides and perimeters

x

and

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

. Prove

x + y \ge 2c

. (You may assume that

\tan \theta \ge \theta

for

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