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Two circles, with centers at points (3, 7) and (−1, 4) and with radii

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Math Expert
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V
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Two circles, with centers at points (3, 7) and (−1, 4) and with radii  [#permalink]

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New post 01 Jun 2020, 08:27
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A
B
C
D
E

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  65% (hard)

Question Stats:

40% (02:10) correct 60% (02:04) wrong based on 43 sessions

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Re: Two circles, with centers at points (3, 7) and (−1, 4) and with radii  [#permalink]

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New post 01 Jun 2020, 11:16
IMO 1
The distance between 2 points = => √(y2-y1)^2+(x2-x1)^2
=> √(7-4)^2+{3-(-1)}^2
=> √(3)^2+(4)^2
=> √9+16 => √25 = 5 units.
The radius of one circle A is 7 and other B is two.
=> the circle B with the centre (3,7) will extend to 2 more units to Z. Making the whole distance from point (-1,4) to the Z will be 7
Circle A and B coincided with each other at point Z
=> There is only one tangent possible from a given point
=> Answer is B

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Re: Two circles, with centers at points (3, 7) and (−1, 4) and with radii  [#permalink]

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New post 01 Jun 2020, 11:41
Bunuel wrote:
Two circles, with centers at points (3, 7) and (−1, 4) and with radii 2 units and 7 units respectively, are drawn in the x-y plane. What is the number of common tangents that the circles can have ?

A. 0
B. 1
C. 2
D. 3
E. 4


Distance between the centers (d) = 5
As d < 2 + 7, the circles should intersect at two distinct points.

Hence, they can have 2 common tangents (option C)

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Re: Two circles, with centers at points (3, 7) and (−1, 4) and with radii  [#permalink]

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New post 01 Jun 2020, 20:17
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1
Bunuel wrote:
Two circles, with centers at points (3, 7) and (−1, 4) and with radii 2 units and 7 units respectively, are drawn in the x-y plane. What is the number of common tangents that the circles can have ?

A. 0
B. 1
C. 2
D. 3
E. 4

Are You Up For the Challenge: 700 Level Questions


Given: Two circles, with centers at points (3, 7) and (−1, 4) and with radii 2 units and 7 units respectively, are drawn in the x-y plane.
Asked: What is the number of common tangents that the circles can have ?

Distance between the centers =\( \sqrt{(3+1)^2 + (7-4)^2} = 5\)

Attachment:
Screenshot 2020-06-02 at 9.46.45 AM.png
Screenshot 2020-06-02 at 9.46.45 AM.png [ 20.42 KiB | Viewed 395 times ]


Since the distance between centers = 5 = 7 - 2

Number of common tangents = 1

IMO B
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Re: Two circles, with centers at points (3, 7) and (−1, 4) and with radii  [#permalink]

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New post 03 Jun 2020, 12:39
IMO B

For the circle with Centre (3,7) and radius 2, one extreme x-axis value =5
Another circle with Centre (-1,4) and radius 7, one extreme x-axis value =5

==> 1st circle is inner circle of 2nd one with both touching at x=5.

So one tangent will be common to both.
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Re: Two circles, with centers at points (3, 7) and (−1, 4) and with radii   [#permalink] 03 Jun 2020, 12:39

Two circles, with centers at points (3, 7) and (−1, 4) and with radii

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