Source: Revised GRE PDF 1st Ed. Section 6: Math; #25 (p. 91)


The figure shows line segment PQ and a

The figure shows line segment PQ and a circle with radius 1 and center 5, 2 in the xy-plane. Which of the following values could be the distance between a point on line segment PQ and a point on the circle? Indicate all such values. 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0

2 Explanations


Angela Sung

Why is the far edge of the circle 5, instead of 6? Isn't the center (5,2) with radius of 1?

Jun 2, 2013 • Comment

Lucas Fink, Magoosh Tutor

Good question, Angela! The far point of the circle is (6,2), it's true. However, that's only 5 away from the line segment QP at minimum, because QP is at the value of 1 on the x-axis. Since 6-1=5, the distance from the middle of QP to the far end of the circle is 5. I hope that helps :-)

Jun 7, 2013 • Reply


Gravatar Chris Lele, Magoosh Tutor

Sep 26, 2012 • Comment

Cristina Velasquez

Hello, Could you please explain how you knew that one of the points was 3.0 of distance away ? Thank you!

Apr 22, 2014 • Reply

Lucas Fink, Magoosh Tutor

Christina— the point on the left side of the circle is 1 away from the center of the circle because the circle has a radius of 1. So that point would be (4,2). that is the closest part of the circle to the line, because it's the point on the circle that is leftmost.

Meanwhile, the point on the line that is closest to the circle is in the center of the line. If you move up or down the line, you can see that it moves away from the circle. That point in the center of the line is (1,2).

We know there is a distance of 3 from those two points— (4,2) (1,2)—by simple subtraction. The y coordinates are the same, so we only care about the 4 and the 1. The distance from 4 to 1 is 3 because 4-1 = 3.

Apr 26, 2014 • Reply

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