chords

[Bryn]

Is the line from the centre of a circle to the midpoint of chord AB always perpendicular to AB?

[Dave]

I believe so, although I can't remember proving it.

 

I think a simple(ish) proof would just be to extend the line to become a radius. Then you know the tangent to the circle at that point is perpendicular and the tangent should be perpendicular to the chord since it passes through the midpoint.

[YT2095]

I gather these aren`t Chords as in a combination of frequencies used in music?

[Dave]

No, a chord on a circle is line AB such that A and B lie on the circumference of the circle.

[YT2095]

ok dokey, just thought I`de ask

[kjitta]

Yes, the midpoint on a chord is the point closest to the centre, therefore a line joining the two points will be perpendicular to the chord.