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

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Math Expert
Joined: 02 Sep 2009
Posts: 48117
In the figure above, if O is the center of the circle, which of the fo  [#permalink]

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11 Dec 2017, 23:08
00:00

Difficulty:

35% (medium)

Question Stats:

83% (00:46) correct 17% (00:56) wrong based on 34 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)

Attachment:

2017-12-12_1001_002.png [ 7.87 KiB | Viewed 513 times ]

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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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12 Dec 2017, 09:09
Bunuel wrote:

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)

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

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