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C is a circle...

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C is a circle...

by avenus » Sun May 03, 2009 6:41 am
C is a circle with center D and radius 2. E is a circle with center F and radius R. Are there any points that are on both E and C?

1)distance from D to F is R+1
2)R=3
Last edited by avenus on Sun May 03, 2009 8:50 am, edited 1 time in total.
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by scoobydooby » Sun May 03, 2009 8:08 am
avenus,
is there are a typo in the question? the question as is seems weird-statement 1) does it say distance between the centers of the circles ie distance between D and F?
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by avenus » Sun May 03, 2009 8:51 am
scoobydooby wrote:avenus,
is there are a typo in the question? the question as is seems weird-statement 1) does it say distance between the centers of the circles ie distance between D and F?
you're right. I've corrected it.
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by scoobydooby » Sun May 03, 2009 10:12 am
1) distance from D to F is R+1
=>if R is 1, then F lies on the circle C and circle C and circle E intersect, there are points on both circles.

if R is say 0.1, then circle E lies inside circle C, no points lie on both circle.
not sufficient

2)R=3
will not have points common to both circle if circles are concentric. circles may be tangent to each other or may intersect each other
not sufficient

together,
distance between D and F is 4, circle E intersects the circle C and passes through mid point of radius of C
=> circles C and E have points in common

hence, C
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by mike22629 » Sun May 03, 2009 11:34 am
Hmm.

I think that it is A.

What is OA?
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by avenus » Mon May 04, 2009 2:18 am
OA is C. I went for A but there's an issue here with the definition of circle. This is what Cambridge's dictionary says about circle:


circle (SHAPE) noun [C]

a continuous curved line, the points of which are always the same distance away from a fixed central point, or the area enclosed by such a line:

Coloured paper was cut into circles, squares and triangles.
We sat in a circle


Depending on which of the two definitions we consider, the answer would be different. So how do we remove the ambiguity?
Any thoughts?
Last edited by avenus on Mon May 04, 2009 1:21 pm, edited 1 time in total.
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by mike22629 » Mon May 04, 2009 9:18 am
I do not understand. Can someone explain further.

The way I see it, no matter what, the end of R has to be only 1 away from the center of the other circle, because R+1 is distance. Therefore, even if R is smallest fraction, it will just be entirely inside the circle.
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by bmlaud » Mon May 04, 2009 10:10 am
The distance between the centres of two circles will determine whether circles intersect or not.
if distance > R + 2 -- non intersecting circles
= R+2-- intersecting at a point
< R+2-- circles intersecting at two points
= 0 --- concentric circles
stat1: distance = R+1 => circles intersect
stat2: R=3 but what's the distance between centres? - can't say
Thus A
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by avenus » Mon May 04, 2009 10:32 am
mike22629 wrote:I do not understand. Can someone explain further.

The way I see it, no matter what, the end of R has to be only 1 away from the center of the other circle, because R+1 is distance. Therefore, even if R is smallest fraction, it will just be entirely inside the circle.
Mike,

I think you're considering the second definition i talked about in my previous post, i.e., circle as the area enclosed in the curved line. If you consider circle as the curved line, then, if R>= 1/2, the two circles (curved lines) will intersect. However, if R< 1/2, F will be inside D (the case you describe) and there's no intersection between the two circles (curved lines).
Does that help?

Anyway, what about the ambiguity posed by the two possible definitions I've mentioned? Who wants to throw some light upon that?
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by dumb.doofus » Mon May 04, 2009 12:34 pm
I think the answer is A

I say so because:

1. Question is not asking if the circles intersect.
2. Question is only asking if there are points that lie on both the circles.

Because it is given that the distance between the center of the circles is R+1, no matter what value of R you take, there will be points that are common to both the circles.
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by avenus » Mon May 04, 2009 1:17 pm
dumb.doofus wrote: 1. Question is not asking if the circles intersect.
2. Question is only asking if there are points that lie on both the circles.
...so what's the difference? If they intersect they obviously have points in common, and vice versa; not sure I understand what you mean.
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by kanha81 » Mon May 04, 2009 1:32 pm
scoobydooby wrote:1) distance from D to F is R+1
=>if R is 1, then F lies on the circle C and circle C and circle E intersect, there are points on both circles.

if R is say 0.1, then circle E lies inside circle C, no points lie on both circle.
not sufficient

2)R=3
will not have points common to both circle if circles are concentric. circles may be tangent to each other or may intersect each other
not sufficient

together,
distance between D and F is 4, circle E intersects the circle C and passes through mid point of radius of C
=> circles C and E have points in common

hence, C
scooby dooby,

I tried to understand your solution, but could not. Is there a way you could explain using a diagram? I tried to sketch the diagram for-


a) 2 circles meet at 1 point
b) Circle C is bigger than circle E and they meet at 1 point

Insuff?
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by benissleeping » Tue May 05, 2009 1:41 am
kanha81 wrote:
scoobydooby wrote:1) distance from D to F is R+1
=>if R is 1, then F lies on the circle C and circle C and circle E intersect, there are points on both circles.

if R is say 0.1, then circle E lies inside circle C, no points lie on both circle.
not sufficient

2)R=3
will not have points common to both circle if circles are concentric. circles may be tangent to each other or may intersect each other
not sufficient

together,
distance between D and F is 4, circle E intersects the circle C and passes through mid point of radius of C
=> circles C and E have points in common

hence, C
scooby dooby,

I tried to understand your solution, but could not. Is there a way you could explain using a diagram? I tried to sketch the diagram for-


a) 2 circles meet at 1 point
b) Circle C is bigger than circle E and they meet at 1 point

Insuff?


Took me a little while but I get it now.

Draw circle C with center D and radius 2. Now assume R=0.1.

Draw center F which is 1.1 from center D. Now draw circle E with radius 0.1 from center F.

You will see that circle E lies completely inside circle C and there are no points common.

As discussed above, the answer will be C.
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