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

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

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New post 11 Oct 2018, 02:03
1
8
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A
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E

Difficulty:

  35% (medium)

Question Stats:

68% (01:26) correct 32% (01:22) wrong based on 97 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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New post 11 Oct 2018, 02:19
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

Answer is A
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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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New post 16 Oct 2018, 11:06
Hi Bunuel,

Could you please post the solution?!

Thanks!
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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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New post 28 Dec 2018, 13:17
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.
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Re: The center of a circle is (10, –3). The point (10, 9) is outside the &nbs [#permalink] 28 Dec 2018, 13:17
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The center of a circle is (10, –3). The point (10, 9) is outside the

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