Expert: Ahmed Salami - 5/31/2004

Question
The point P is any point placed inside a circle.  Is it always possible to draw a line through P that is bisected at the point P? Explain.

Answer
Hi,
Well, you didn't exactly mention any restrictions to how this line is drawn especially with regards to the circle.
Therefore it is always possible to draw this line. All you have to do is make sure the centre of the line coincides with this point.
Even if this line has to have its ends on the circumference of the circle, it could always be possible. This line has to be one that is perpendicular to the the line joining the centre of the circle to the point P and of course at the same time touching P.
If the point P is the centre of the circle, then any diameter would do.

I hope this helps.
You can always acknowledge.