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## 'The Line and Its Strange Pair' printed from http://nrich.maths.org/

This problem builds on from

Points in Pairs - 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
along the dotted line.

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

If P' moves along a straight line what does P do?

Why?

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