Find the ratio of the lengths of the chords?

[chijioke]

Two chords of a circle of radius 10 cm are 3 cm apart. If the middle chord is 2 cm away from the centre, find the ratio of the lengths of the chords?
My attempt to the problem is attached below:

If the solution is correct, can the ratio be left as [math]8 \sqrt{ 6 } : 5 \sqrt{ 15 } : \sqrt{ 399 }[/math] ?

 

[Dr.Peterson]

Two chords of a circle of radius 10 cm are 3 cm apart. If the middle chord is 2 cm away from the centre, find the ratio of the lengths of the chords?
My attempt to the problem is attached below:
View attachment 34985
If the solution is correct, can the ratio be left as [math]8 \sqrt{ 6 } : 5 \sqrt{ 15 } : \sqrt{ 399 }[/math] ?

Did you mean to say "three chords"??

Three chords of a circle of radius 10 cm are 3 cm apart. If the middle chord is 2 cm away from the centre, find the ratio of the lengths of the chords?​

I would interpret "three chords are 3 cm apart" as meaning there are 3 cm between the top two chords, and 3 cm between the bottom two chords.

Taking it your way, I see no basis for your distances of 1/2 cm; the problem couldn't be solved.

 

[chijioke]

Did you mean to say "three chords"??

Three chord was not mentioned earlier, in the first sentence. It was implied in the the second sentence where it says If the middle chord is 2 cm away from the centre...

Three chords of a circle of radius 10 cm are 3 cm apart. If the middle chord is 2 cm away from the centre, find the ratio of the lengths of the chords?​

I would interpret "three chords are 3 cm apart" as meaning there are 3 cm between the top two chords, and 3 cm between the bottom two chords.

Taking it your way, I see no basis for your distances of 1/2 cm; the problem couldn't be solved.

Okay.

 

[Dr.Peterson]

Three chord was not mentioned earlier, in the first sentence. It was implied in the the second sentence where it says If the middle chord is 2 cm away from the centre...

If it says exactly what you wrote (I assume you are not translating these problems), then it is very poorly written; "the middle chord" implies it has been mentioned before. We might assume that "the middle chord" is a third chord exactly between the first two, so that the chords are spaced at 1.5 inches (so they would all be on the same side of the center); otherwise, there is not enough information. Or, "the middle chord" might mean the one closer to the center, of the two that were mentioned.

I don't think this one is worth spending time on. Where do these problems come from?