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circumference of radius 1

Source: China TST 1991, problem 4

June 27, 2005

geometry unsolvedgeometry

Problem Statement

We choose 5 points

A_1, A_2, \ldots, A_5

on a circumference of radius 1 and centre

O.

P

is a point inside the circle. Denote

Q_i

as the intersection of

A_iA_{i+2}

and

A_{i+1}P

, where

A_7 = A_2

and

A_6 = A_1.

Let

OQ_i = d_i, i = 1,2, \ldots, 5.

Find the product

\prod^5_{i=1} A_iQ_i

in terms of

d_i.

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