Practice GMAT Problem Solving Question
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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.
Correct Answer: D
- 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.
- 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 = πr2
rA = 12 = radius of circle A
dA = 2(12) = 24 = diameter of circle A
Area of B = 169π = πr2
rB = 13 = radius of circle B
dB = 2(13) = 26 = diameter of circle B - Maximum distance of xy = 24 + 26 = 50
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