MathDB

Label the vertices of a trapezoid

T

inscribed in the unit circle as

A,B,C,D

counterclockwise with

AB\parallel CD

. Let

s_1,s_2,

and

d

denote the lengths of

AB

CD

, and

OE

, where

E

is the intersection of the diagonals of

T

, and

O

is the center of the circle. Determine the least upper bound of

\frac{s_1-s_2}d

over all

T

for which

d\ne0

, and describe all cases, if any, in which equality is attained.

B5