Find the distance between the chords.

[chijioke]

Here is my diagram. Is it correct?

 

[stapel]

As drawn, the length of [imath]h[/imath] can vary, depending upon its angle with respect to the chords. I *think* you're supposed to assume that the chords are parallel... but I could be wrong.

 

[chijioke]

But it is written that the chords are at alternate side of the circle.

 

[pka]

View attachment 35896
Here is my diagram. Is it correct?
View attachment 35897

What does "alternate side of the circle" mean?

 

[Dr.Peterson]

But it is written that the chords are at alternate side of the circle.

I suppose they mean "opposite sides", and specifically, exactly opposite, so that the chords are parallel. That is also necessary in order for the distance between the chords to make sense, since the distance between lines is measured perpendicular to both, if possible.

This is a very poorly written problem.

(In addition, "alternate" and "alternative" are different words; your word choice makes more sense than theirs, but still doesn't have the right meaning.)

 

[chijioke]

What does "alternate side of the circle" mean?

I think it means as I have show in op.

 

[Dr.Peterson]

I think it means as I have show in op.

But your h makes no sense.

 

[chijioke]

Does this one now make sense?

 

[pka]

But it is written that the chords are at alternate side of the circle.

If you read this LINK. Because the chords are of different lengths you must find the distance each is from the centre.
Then add those together to get their distance apart.

 

[blamocur]

View attachment 35900
Does this one now make sense?

It makes more sense since your cords look "more parallel". A minor quibble: the AOD line (where O is the center of the circle) looks like a straight line, which it would not be for chords of different size.

 

[chijioke]

If you read this LINK. Because the chords are of different lengths you must find the distance each is from the centre.
Then add those together to get their distance apart.

Let h1 be the distance of chord AB from centre of circle.
h2= distance of chord CD from centre of circle.

[math]h1= \sqrt{36-25}=\sqrt{11}[/math]
[math]h2= \sqrt{36-9}=\sqrt{27}[/math]Distance between the two chords is [math]\sqrt{11}+\sqrt{27} =8.5~cm[/math]

 

[blamocur]

Looks good to me.

 

[The Highlander]

Distance between the two chords is [math]\sqrt{11}+\sqrt{27} =8.5~cm[/math]

You're doing it again![math]\sqrt{11}+\sqrt{27}\ne 8.5~cm[/math]
[math]\sqrt{11}+\sqrt{27}\approx 8.5~cm[/math]

or \(\displaystyle ~\sqrt{11}+\sqrt{27} =8.5~cm\) to 1 d.p. (or 2 s.f.)​

 

[chijioke]

Thanks for reminding me once again. I believe I will not do it again.