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605-655 Level|   Geometry|      
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atalpanditgmat
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The radii of two circles are 2 inches and 4 inches, respecti Updated on: 16 Jun 2013, 04:47
Originally posted by atalpanditgmat on 16 Jun 2013, 04:43.
Last edited by Bunuel on 16 Jun 2013, 04:47, edited 1 time in total.
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The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Guys if possible illustrate graphically...

Thanks
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Bunuel
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The radii of two circles are 2 inches and 4 inches, respecti 16 Jun 2013, 04:52
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atalpanditgmat
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Guys if possible illustrate graphically...

Thanks

The wording is not perfect, but anyway... Both statements basically imply the same case:
Attachment:
Circles.png
Circles.png [ 13.99 KiB | Viewed 3927 times ]

Hope it helps.
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The radii of two circles are 2 inches and 4 inches, respecti 16 Jun 2013, 05:14
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Bunuel
atalpanditgmat
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Guys if possible illustrate graphically...

Thanks

The wording is not perfect, but anyway... Both statements basically imply the same case:
Attachment:
Circles.png

Hope it helps.


statement 2 never said "center of larger circle lies on circumference of the smaller circle" then how diagram is same for statement also?
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The radii of two circles are 2 inches and 4 inches, respecti 16 Jun 2013, 05:25
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aakashkumar212
Bunuel
atalpanditgmat
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Guys if possible illustrate graphically...

Thanks

The wording is not perfect, but anyway... Both statements basically imply the same case:
Attachment:
Circles.png

Hope it helps.


statement 2 never said "center of larger circle lies on circumference of the smaller circle" then how diagram is same for statement also?

A circle is a line forming a closed loop, every point on which is a fixed distance from a center point.

Therefore, on the circle = on the line (curve).

Hope it's clear.
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The radii of two circles are 2 inches and 4 inches, respecti 16 Jun 2013, 05:38
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Thanks Bunuel. It is much clearer now...
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The radii of two circles are 2 inches and 4 inches, respecti 16 Jun 2013, 21:45
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Bunuel
atalpanditgmat
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Guys if possible illustrate graphically...

Thanks

The wording is not perfect, but anyway... Both statements basically imply the same case:
Attachment:
Circles.png

Hope it helps.

What software do you use to illustrate bunuel?
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The radii of two circles are 2 inches and 4 inches, respecti 16 Jun 2013, 22:39
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atalpanditgmat
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Guys if possible illustrate graphically...

Thanks

The wording is not perfect, but anyway... Both statements basically imply the same case:
Attachment:
Circles.png

Hope it helps.

What software do you use to illustrate bunuel?

Online graph plotter: https://graph-plotter.cours-de-math.eu/ Though for this particular question I just borrowed xy-plane from there and used Paint to draw the circles.

I also highly recommend computational knowledge engine Wolfram Alpha: https://www.wolframalpha.com/
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The radii of two circles are 2 inches and 4 inches, respecti 10 Dec 2013, 14:35
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The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Maybe the wording is a bit incorrect, but couldn't 1) mean that the circles touch overlapping one another, where, for example, the smaller circle intersects the larger circle at two points or does it mean they can only have one point of intersection?
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The radii of two circles are 2 inches and 4 inches, respecti 11 Dec 2013, 00:17
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WholeLottaLove
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Maybe the wording is a bit incorrect, but couldn't 1) mean that the circles touch overlapping one another, where, for example, the smaller circle intersects the larger circle at two points or does it mean they can only have one point of intersection?
That's what even I was thinking.

Plus, another question. How can we determine the distances between the centres by just knowing whether they touch each other or not?
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The radii of two circles are 2 inches and 4 inches, respecti 11 Dec 2013, 03:26
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WholeLottaLove
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Maybe the wording is a bit incorrect, but couldn't 1) mean that the circles touch overlapping one another, where, for example, the smaller circle intersects the larger circle at two points or does it mean they can only have one point of intersection?

You can interpret "touch" as intersect at one point.
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The radii of two circles are 2 inches and 4 inches, respecti 11 Dec 2013, 03:26
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WholeLottaLove
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Maybe the wording is a bit incorrect, but couldn't 1) mean that the circles touch overlapping one another, where, for example, the smaller circle intersects the larger circle at two points or does it mean they can only have one point of intersection?
That's what even I was thinking.

Plus, another question. How can we determine the distances between the centres by just knowing whether they touch each other or not?

Refer to the diagram in my post above.
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The radii of two circles are 2 inches and 4 inches, respecti 11 Dec 2013, 04:03
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WholeLottaLove
The radii of two circles are 2 inches and 4 inches, respectively. What is the distance between their centres?

(1) The two circles touch internally.
(2) The centre of the larger circle lies on the smaller circle.

Maybe the wording is a bit incorrect, but couldn't 1) mean that the circles touch overlapping one another, where, for example, the smaller circle intersects the larger circle at two points or does it mean they can only have one point of intersection?
That's what even I was thinking.

Plus, another question. How can we determine the distances between the centres by just knowing whether they touch each other or not?

Refer to the diagram in my post above.
So you mean to say, centre of the smaller circle touching the bigger circle internally, the distances between their centres will always be the same (thus forming another circle)?
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The radii of two circles are 2 inches and 4 inches, respecti 11 Dec 2013, 04:10
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Bunuel
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That's what even I was thinking.

Plus, another question. How can we determine the distances between the centres by just knowing whether they touch each other or not?

Refer to the diagram in my post above.
So you mean to say, centre of the smaller circle touching the bigger circle internally, the distances between their centres will always be the same (thus forming another circle)?

I don't understand what you mean Please elaborate.
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The radii of two circles are 2 inches and 4 inches, respecti 11 Dec 2013, 06:29
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I don't understand what you mean Please elaborate.
For statement number 1 that we have: Two circles touch internally.

Will the distance between their centers always be the same?
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The radii of two circles are 2 inches and 4 inches, respecti 11 Dec 2013, 07:51
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Bunuel
I don't understand what you mean Please elaborate.
For statement number 1 that we have: Two circles touch internally.

Will the distance between their centers always be the same?

Yes, the distance will be the same. If you roll the smaller circle its center will be moving around green circle below:
Attachment:
Cricles.png
Cricles.png [ 18.91 KiB | Viewed 3482 times ]
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The radii of two circles are 2 inches and 4 inches, respecti 29 Mar 2016, 18:28
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i don't think the wording is appropriate.
the 2 circles might have 2 points of intersection.
the distance might be 2, or might be even more
so together with statement 2, we can see that there is only 1 point of intersection, and on the other side from the point is the origin of the bigger circle...
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The radii of two circles are 2 inches and 4 inches, respecti 11 Aug 2019, 22:35
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