32

Part of 1970 IMO Longlists

Problems(1)

Determine the behavior of t_i for i→∞.

Source: IMO LongList 1970 - P32

Let there be given an acute angle

\angle AOB = 3\alpha

\overline{OA}= \overline{OB}

A

is the center of a circle with radius

\overline{OA}

s

OA

B

. Inside the given angle a variable line

t

is drawn through

O

. It meets the circle in

O

C

and the given line

s

D

\angle AOC = x

. Starting from an arbitrarily chosen position

t_0

t

t_0, t_1, t_2, \ldots

is determined by defining

\overline{BD_{i+1}}=\overline{OC_i}

i

C_i

D_i

denote the positions of

C

D

, corresponding to

t_i

). Making use of the graphical representations of

BD

OC

as functions of

x

, determine the behavior of

t_i

i\to \infty

functiongeometry unsolvedgeometry