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In the figure above, if O is the center of the circle, which of the fo

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In the figure above, if O is the center of the circle, which of the fo [#permalink]

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New post 11 Dec 2017, 23:08
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Question Stats:

81% (00:40) correct 19% (00:42) wrong based on 25 sessions

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In the figure above, if O is the center of the circle, which of the following points lies outside the circle?

(A) (–7, –8)
(B) (–7, 7)
(C) (8, –6)
(D) (8, 5)
(E) (9, 4)

[Reveal] Spoiler:
Attachment:
2017-12-12_1001_002.png
2017-12-12_1001_002.png [ 7.87 KiB | Viewed 407 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, if O is the center of the circle, which of the fo [#permalink]

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New post 12 Dec 2017, 09:09
Bunuel wrote:
Image
In the figure above, if O is the center of the circle, which of the following points lies outside the circle?

(A) (–7, –8)
(B) (–7, 7)
(C) (8, –6)
(D) (8, 5)
(E) (9, 4)

[Reveal] Spoiler:
Attachment:
2017-12-12_1001_002.png

One quick way to approach this question: add the squares of the coordinates in the answers. They should not be greater than 100. (I avoid the distance formula when there are less error-prone ways to solve.)

The general equation for a line is \(x^2 + y^2 = r^2\).

This circle's radius is 10 (center x-coordinate is at 0, a point on the circle is (10,0), subtract x-coordinates).

So this line's equation is \(x^2 + y^2 = 100\).

A point outside the circle will have coordinates whose squares sum to more than 100.

\(x^2 + y^2 = 100\)

(A) (–7, –8)
\((-7)^2 + 8^2 = 49 + 64 = 113\)
Outside the circle. Keep

(B) (–7, 7)
\(49 + 49 = 98\). Inside the circle. Reject

(C) (8, –6)
\(64 + 36 = 100\). On the circle. Reject

(D) (8, 5)
\(64 + 25 = 89\). Inside the circle. Reject

(E) (9, 4)
\(81 + 16 = 97\). Inside the circle. Reject

Answer A
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Re: In the figure above, if O is the center of the circle, which of the fo   [#permalink] 12 Dec 2017, 09:09
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