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# The center of a circle is (10, –3). The point (10, 9) is outside the

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Math Expert
Joined: 02 Sep 2009
Posts: 55670
The center of a circle is (10, –3). The point (10, 9) is outside the  [#permalink]

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11 Oct 2018, 03:03
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8
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Difficulty:

35% (medium)

Question Stats:

71% (01:57) correct 29% (02:17) wrong based on 115 sessions

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The center of a circle is (10, –3). The point (10, 9) is outside the circle, and the point (6, –3) is inside the circle; neither point is on the circle. If the radius, r, is an integer, how many possible values are there for r?

(A) Seven
(B) Eight
(C) Nine
(D) Ten
(E) Eleven

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Re: The center of a circle is (10, –3). The point (10, 9) is outside the  [#permalink]

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11 Oct 2018, 03:19
as the point (10,9) is outside the circle and point (6,3) is inside the circle so max value of radius will be difference in y coordinate value. so max. radius=9-(-3)=9+3=12
as point (10,-3) can't be on the circle so max radius will be 11.999...
and minimum value of radius will be 10-5.9=4.1
so total values of radius are in between 4.1 and 11.9 = 7 values

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Joined: 18 Jul 2018
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Re: The center of a circle is (10, –3). The point (10, 9) is outside the  [#permalink]

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16 Oct 2018, 12:06
Hi Bunuel,

Could you please post the solution?!

Thanks!
Intern
Joined: 30 Nov 2018
Posts: 7
Re: The center of a circle is (10, –3). The point (10, 9) is outside the  [#permalink]

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28 Dec 2018, 14:17
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1
plot the coordinates on the graph,
(6,-3) lies inside, so the distance on x axis is 4 so the radius should be more than that r>4

(10,9) lies outside the graph, distance on y is 12( max ) so the radius has to be less than that r<12

so 4<r<12, r can take seven values.
Re: The center of a circle is (10, –3). The point (10, 9) is outside the   [#permalink] 28 Dec 2018, 14:17
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# The center of a circle is (10, –3). The point (10, 9) is outside the

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