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In the xyplane, the point with coordinates is the center of [#permalink]
18 Jan 2016, 16:03
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In the xyplane, the point with coordinates (−6, −7) is the center of circle C. The point with coordinates (−6, 5) lies inside C, and the point with coordinates (8, −7) lies outside C. If m is the radius of C and m is an integer, what is the value of m ? \(M=\) Practice Questions Question: 14 Page: 341 Difficulty: medium
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Re: In the xyplane, the point with coordinates is the center of [#permalink]
18 Jan 2016, 16:05
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Solution
In this question you are given that the point with coordinates (−6,−7) is the center of circle C, the point with coordinates (−6, 5) lies inside circle C, and the point with coordinates (8,−7) lies outside circle C, so you could draw the following figure. From the figure, you can see that the distance between (−6,−7) and (−6, 5) is 7+5, or 12, and the radius of C must be greater than 12. You can also see that the distance between (−6,−7) and (8,−7) is 6+8, or 14, and the radius of C must be less than 14. Therefore, since the radius is an integer greater than 12 and less than 14, it must be 13. The correct answer is \(13.\)
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Re: In the xyplane, the point with coordinates is the center of [#permalink]
11 Jan 2019, 23:25
Carcass wrote: In the xyplane, the point with coordinates (−6, −7) is the center of circle C. The point with coordinates (−6, 5) lies inside C, and the point with coordinates (8, −7) lies outside C. If m is the radius of C and m is an integer, what is the value of m ? \(M=\) Practice Questions Question: 14 Page: 341 Difficulty: medium we can see that the coordinates (−6, 5) inside C has xcoord same as centre (6, 7), thus the difference in ycoord will give us the line of radius... Since (6, 5) is inside the circle, the radius is GREATER than the difference in ycoord, =>\(r>5(7)=12\) we can also see that the coordinates (8, −7) outside C have ycoord same as centre (6, 7), thus the difference in xcoord will give us the line of radius... Since (8, −7) is outside the circle, the radius is LESSER than the difference in xcoord, =>\(r<8(6)=14\) Thus \(12<r<14\), and as r is an integer, only 13 fits in
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html



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Re: In the xyplane, the point with coordinates is the center of [#permalink]
13 Jan 2019, 02:13
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List the points
Center = (6,7) Inside = (6,5) Outside= (8,7)
use the distance formula for each point's distance from the center. Start with distance from inside to center, and you'll see that they have the same x coordinate, which means your x distance is o then you just have to calculate \sqrt{(75)^2}=12 Now do the same thing with distance from outside circle to inside. they have the same y coordinate of 7, so just calculate the distances of the x coordinate \sqrt{(68)^2} =14
which means the radius has to be the only integer between 12 and 14, which is 13




Re: In the xyplane, the point with coordinates is the center of
[#permalink]
13 Jan 2019, 02:13





