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BMAD

Circles and Chords a theory

Question

How many circles exist with the following properties...

1. Contains two chords that are 2 cm from each other

2. The longer chord only gets as close as 1 cm from the center.

3. The shorter chord only gets as close as 3 cm from the center.

versus

How many circles exist with the following properties...

1. Contains two chords that only gets as close as 2 cm from each other.

2. The longer chord only gets as close as 1 cm from the center.

3. The shorter chord only gets as close as 3 cm from the center.

Edited by BMAD

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1 hour ago, BMAD said:

How many circles exist with the following properties...

1. Contains two chords that are 2 cm from each other

2. The longer chord only gets as close as 1 cm from the center.

3. The shorter chord only gets as close as 3 cm from the center.

versus

How many circles exist with the following properties...

1. Contains two chords that only gets as close as 2 cm from each other.

2. The longer chord only gets as close as 1 cm from the center.

3. The shorter chord only gets as close as 3 cm from the center.

I forgot, say the smaller chord is 5 cm in length and the bigger chord 7 cm in length 

Edited by BMAD

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Spoiler

A circle that has a chord of length of 2c that gets as close as r to its center has a radius of sqrt( r 2 + c 2).

A circle with a 7cm chord that gets as close as 1cm to its center has a radius of 3.640 cm (red circle)
A circle with a 5cm chord that gets as close as 3cm to its center has a radius of 3.905 cm (blue circle)

Since these are different circles, the answer to both questions is zero.

5-7B.jpg

The green circles have radii (distances from center) of 1 and 3, and the chords have lengths 7 and 5, respectively

If the chords are not parallel, their distance becomes less than 2 cm.

 

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4 hours ago, bonanova said:
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A circle that has a chord of length of 2c that gets as close as r to its center has a radius of sqrt( r 2 + c 2).

A circle with a 7cm chord that gets as close as 1cm to its center has a radius of 3.640 cm (red circle)
A circle with a 5cm chord that gets as close as 3cm to its center has a radius of 3.905 cm (blue circle)

Since these are different circles, the answer to both questions is zero.

5-7B.jpg

The green circles have radii (distances from center) of 1 and 3, and the chords have lengths 7 and 5, respectively

If the chords are not parallel, their distance becomes less than 2 cm.

 

I disagree with your conclusion in the second case.

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On 6/15/2016 at 8:27 AM, BMAD said:

I disagree with your conclusion in the second case.

The conclusion that they must be parallel?

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3 hours ago, bonanova said:

The conclusion that they must be parallel?

i disagree with this line:

If the chords are not parallel, their distance becomes less than 2 cm.

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On 6/17/2016 at 11:00 AM, BMAD said:

i disagree with this line:

If the chords are not parallel, their distance becomes less than 2 cm.

Of course you're right. I needlessly put the chords on the same side of center.

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