In the above figure, the area of circle A is 144π and the area of circ

Question

https://gmatclub.com/forum/download/file.php?id=27071 In the above figure, the area of circle A is 144π and the area of circle B is 169π. If point x (not shown above) lies on circle A and point y (not shown above) lies on circle B, what is the range of the possible lengths of line xY. A) 0 to 169π^2 B) 0 to 144 C) 0 to 25 D) 0 to 50 E) 5 to 144 Source: Platinum GMAT Kudos for a correct solution . 00022-1.gif

reto · Answer

Circle A has a Diameter of 24
Circle B has a Diameter of 26

Shortest line, if both points lie in the middle where the circles tangent = 0. If both points lie on the outer bounds, then the longest line would be their diameters 26 + 24 = 50.

Answer D.

GMATinsight · Answer

Area of Circle = πr^2

Area of Circle A = 144π = πr^2
i.e. Radius of Circle A = 12

Area of Circle B = 169π = πr^2
i.e. Radius of Circle B = 13

Maximum Length of XY = Diameter of A + Diameter of B = 2(12+13) = 50
Minimum Length of XY = 0 (When the Two circles are tangent to each other)

Answer: Option  D

KS15 · Answer

Area of circle A=144pie
Therefore, radius=12 and diameter=24
Similarly, radius of circle B=13 and diameter=26
If both the points X and Y lie on the same point, distance=0
For max distance, we need to add the distance of diameters=24+26=50
Answer D

lipsi18 · Answer

Area of A = 144pie = pie r^2 =? r=12; d=24
Area of B=169pie=pie R^2 => R=13; D=26
Minimum length of length of xy = 0, where both A and B touches 
Maximum length of XY = d+D=50,
Hence range of length of xy = 0 to 50

Hence answer is D
Thanks,

Bunuel · Answer

Platinum GMAT Official Solution: The shortest distance of line xy will occur when x and y are at the same point (i.e., the point where the two circles come together). In this instance, the line xy will be 0 units long. In order to determine the longest possible distance for xy, we must first recall that the longest line across a circle is the circle's diameter. In other words, it is impossible to construct a line from one point on a circle to another point on the same circle that is longer than the circle's diameter. The longest distance of line xy will occur when x and y are at exact opposite sides of the two circles. In other words, when x is at the far left of A and y is at the far right of B. More technically, line xy will be the combined diameter of circles A and B. This makes sense given that the diameter of a circle is the longest possible line from one point on the circle to another point on the same circle. https://gmatclub.com/forum/download/file.php?id=27092 Since the length of xy is the length of the diameter of A plus the diameter of B, we need to find the diameter of each circle. Area of A = 144π = πr^2 rA = 12 = radius of circle A dA = 2(12) = 24 = diameter of circle A Area of B = 169π = πr^2 rB = 13 = radius of circle B dB = 2(13) = 26 = diameter of circle B Maximum distance of xy = 24 + 26 = 50. Answer: D. 00022-2.gif

bumpbot · Answer

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In the above figure, the area of circle A is 144π and the area of circ

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In the above figure, the area of circle A is 144π and the area of circ

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