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Re: Two circles overlap such that the center of each circle lies on the ci [#permalink]

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12 Feb 2015, 20:20

1

This post received KUDOS

Statement 1 : Since The longest distance between any two points on the circles is 9 and Two circles overlap such that the center of each circle lies on the circumference of the other .

Assuming radius of circle is r , 3 R = 9 => R = 3 .

Two circles overlap such that the center of each circle lies on the circumference of the other. What is the circumference of one circle?

(1) The longest distance between any two points on the circles is 9. (2) The area of one circle is 9π.

Kudos for a correct solution.

When two circles overlap such that their centers are on each other's circumference, their radii will be equal. The diagram will help you understand this.

Attachment:

Ques3.jpg [ 7.42 KiB | Viewed 2683 times ]

Besides, the format of the question should give you a hint that the circumference of the two circles should be the same. "What is the circumference of one circle?" If the two circles had difference radii, they would have specified the circle for which they wanted the circumference or they would have asked for the circumferences of the two circles.

Circle1 has center at C1 and its radius will be the distance of C1 from its circumference. One point on the circumference is C2 so its radius will be equal to distance between C1 and C2. Similarly, the radius of circle 2 will be distance between C2 and C1. Hence both will have the same radii. To get circumference, all you need is the value of any one defined aspect of the circles. Statement 1 gives you the diameter which gives you the circumference. Statement 2 gives you the area of the circles which gives you the radius and hence the circumference.

Re: Two circles overlap such that the center of each circle lies on the ci [#permalink]

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13 Feb 2015, 00:09

VeritasPrepKarishma wrote:

Bunuel wrote:

Two circles overlap such that the center of each circle lies on the circumference of the other. What is the circumference of one circle?

(1) The longest distance between any two points on the circles is 9. (2) The area of one circle is 9π.

Kudos for a correct solution.

When two circles overlap such that their centers are on each other's circumference, their radii will be equal. The diagram will help you understand this.

Attachment:

Ques3.jpg

Besides, the format of the question should give you a hint that the circumference of the two circles should be the same. "What is the circumference of one circle?" If the two circles had difference radii, they would have specified the circle for which they wanted the circumference or they would have asked for the circumferences of the two circles.

Circle1 has center at C1 and its radius will be the distance of C1 from its circumference. One point on the circumference is C2 so its radius will be equal to distance between C1 and C2. Similarly, the radius of circle 2 will be distance between C2 and C1. Hence both will have the same radii. To get circumference, all you need is the value of any one defined aspect of the circles. Statement 1 gives you the diameter which gives you the circumference. Statement 2 gives you the area of the circles which gives you the radius and hence the circumference.

Answer (D)

Hi

So, as per Stmnt 1, Will the Radius be 9 ? As it says that distance between any two points on the circles is 9

I marked Stmnt 1 - Insufficient initially but later figured out my mistake

So, as per Stmnt 1, Will the Radius be 9 ? As it says that distance between any two points on the circles is 9

I marked Stmnt 1 - Insufficient initially but later figured out my mistake

No, the radius will be 3.

The longest distance between any two points on the circles will be the distance between two points which are farthest away from each other (considering both the circles together). If you extend the line C1C2 on both sides, the points where they intersect the circles will be farthest from each other. The distance between those points will be diameter+radius = 9 3*radius = 9 Radius = 3
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Let’s draw this shape. We know the circles are the same size and will form what looks like a Venn diagram:

Attachment:

Picture_1.png [ 13.55 KiB | Viewed 2587 times ]

The formula for circumference is 2πr. The only piece of information we need to find the circumference is to know the radius of one of the circles.

Statement (1) tells us the radius because we know this “longest distance” will be made up of 3 radii. 3r = 9, so the radius must be 3. Sufficient.

Statement (2) gives us the radius since the formula for area of a circle is πr^2. If πr^2=9π, then the radius is 3. Sufficient.

If you chose (A), this is sufficient, but Statement (2) is also sufficient. If we know the area, we know the radius.

If you chose (B), you didn’t realize that the longest distance between any two points in a circle lies along the diameter. This this “longest distance” between the two circles will be equal to three times the radius.

If you chose (C), there’s no need to combine here as each statement individually allows us to find the radius. Once we have the radius, we can find the circumference.

If you chose (E), you may want to review the formulas for circumference and area of a circle. You may also have missed the fact that the circles would need to be the same size according to the given information.
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Re: Two circles overlap such that the center of each circle lies on the ci [#permalink]

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17 Feb 2015, 03:52

A gives us the value of diameter so we can find the circumference ..if we draw the circles then both circles will have equal radius.Hence sufficient. B gives the area of one circle so we an find the circumference. hence sufficient . ANS D.

Re: Two circles overlap such that the center of each circle lies on the ci [#permalink]

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29 Oct 2017, 17:19

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