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# The figure shows line segment PQ and a circle with radius 1 and center

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Math Expert
Joined: 02 Sep 2009
Posts: 55801
The figure shows line segment PQ and a circle with radius 1 and center  [#permalink]

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23 May 2019, 21:34
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:28) correct 27% (01:46) wrong based on 15 sessions

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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?

I. 2.5
II. 3.0
III. 5.5

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Attachment:

#GREpracticequestion The figure shows line segment PQ .jpg [ 12.23 KiB | Viewed 255 times ]

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Re: The figure shows line segment PQ and a circle with radius 1 and center  [#permalink]

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23 May 2019, 21:48
Bunuel wrote:

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?

I. 2.5
II. 3.0
III. 5.5

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Attachment:
The attachment #GREpracticequestion The figure shows line segment PQ .jpg is no longer available

Check max and min distance possible. 3<d<5
Attachment:

IMG_20190524_101604__01.jpg [ 1.93 MiB | Viewed 175 times ]

B. Only II
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Re: The figure shows line segment PQ and a circle with radius 1 and center  [#permalink]

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23 May 2019, 22:15
1
Bunuel wrote:

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?

I. 2.5
II. 3.0
III. 5.5

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Attachment:
#GREpracticequestion The figure shows line segment PQ .jpg

Min distance is 3 (mid point of PQ {1,2} to point {4,2})
Max distance is $$\sqrt{26}$$ (P to point {6,2} on circle; Note that Point {6,2}, midpoint of PQ{4,2} and P makes a right triangle)
$$3\leq Distance\leq\sqrt{26}$$. Only II falls in this range. Therefore B.
Re: The figure shows line segment PQ and a circle with radius 1 and center   [#permalink] 23 May 2019, 22:15
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