MathDB

Let

A

and

B

be the endpoints of a semicircular arc of radius

2

. The arc is divided into seven congruent arcs by six equally spaced points

C_1,C_2,\ldots,C_6

. All chords of the form

\overline{AC_i}

\overline{BC_i}

are drawn. Let

n

be the product of the lengths of these twelve chords. Find the remainder when

n

is divided by

1000

Problem Statement