Copyright © University of Cambridge. All rights reserved.

## 'Mapping the Wandering Circle' printed from http://nrich.maths.org/

This problem builds on from

The Line and Its Strange Pair - you
may wish to look at that first.

Two points, one inside a circle and the other outside, are
related in the following way :

A line starting at the centre of the circle and passing through
the first point ( P ) goes on to pass through the second point ( P'
)

Positions along the line are such that the ratio of OP to the
radius of the circle matches the ratio of the radius of the circle
to OP'

For example if OP happened to be 2/3 of the radius then OP'
would be 3/2 of the radius.

In the diagram above, the point P can move to different places
around the dotted circle.

Each position P takes will fix a corresponding position for P'
.

As P moves around that circle what will P' do ?

Why?

You might find the interactivity below helpful.
Holding down the mouse button leaves a trace of the points.

**If you can see this message Flash may not be working in your browser**
**Please see http://nrich.maths.org/techhelp/#flash to enable it.**