MathDB

Let

w

be a circle and

AB

a line not intersecting

w

. Given a point

P_{0}

w

, define the sequence

P_{0},P_{1},\ldots

as follows: P_{n\plus{}1} is the second intersection with

w

of the line passing through

B

and the second intersection of the line

AP_{n}

with

w

. Prove that for a positive integer

k

, if P_{0}\equal{}P_{k} for some choice of

P_{0}

, then P_{0}\equal{}P_{k} for any choice of

P_{0}

.
Gheorge Eckstein

Problem Statement