14

Part of 2000 Harvard-MIT Mathematics Tournament

Problems(2)

2000 Guts #14: Cyclic quadrilateral

Source:

ABCD

is a cyclic quadrilateral inscribed in a circle of radius

5

AB=6

BC=7

CD=8

AD

trigonometrygeometry

2000 HMMT RMT Team #14

Source:

Define a sequence

<x_n>

of real numbers by specifying an initial

x_0

and by the recurrence

x_{n+1}=\frac{1+x_n}{1-x_n}

x_n

as a function of

x_0

n

, in closed form. There may be multiple cases.