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In the figure above, the circle with center O has diameter 10 and the

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In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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16 Nov 2017, 07:30
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5% (low)

Question Stats:

92% (00:31) correct 8% (00:53) wrong based on 76 sessions

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In the figure above, the circle with center O has diameter 10 and the circle with center P has diameter 6. If the two circles are tangent to each other, what is the length of the segment OP?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 20

Attachment:

2017-11-16_1929.png [ 5.7 KiB | Viewed 1311 times ]

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Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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16 Nov 2017, 07:55
A. 8

OP=10/2+6/2 =8

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Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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16 Nov 2017, 07:55
Think the answers is A here.

Circle O ==> D=10 so R=5
Circle P ==> D=6 so R=3

O and P are tangent, so no distance between them. 5+3 = 8, hence A.
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Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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16 Nov 2017, 08:32
$$\frac{10+6}{2} = 8$$

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Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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16 Nov 2017, 08:51
OM=5 PM=3
OP=5+3=8
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Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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16 Nov 2017, 12:05
Bunuel wrote:

In the figure above, the circle with center O has diameter 10 and the circle with center P has diameter 6. If the two circles are tangent to each other, what is the length of the segment OP?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 20

Attachment:
2017-11-16_1929.png

Two circles tangent to each other share a common tangent line at the point of tangency.

At that point, the common tangent line is perpendicular to the radius of each circle.

Therefore, the radii and the point of tangency lie on the same line, which is why we can add the lengths of the radii to get the length of OP.

2r = diameter
OP = (3+5) = 8

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Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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17 Nov 2017, 13:26
Bunuel wrote:

In the figure above, the circle with center O has diameter 10 and the circle with center P has diameter 6. If the two circles are tangent to each other, what is the length of the segment OP?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 20

We see that the radius of circle O is 5 and the radius of circle P is 3; thus, the length of segment OP is 8.

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Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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02 Dec 2017, 02:07
1
Bunuel wrote:

In the figure above, the circle with center O has diameter 10 and the circle with center P has diameter 6. If the two circles are tangent to each other, what is the length of the segment OP?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 20

Attachment:
2017-11-16_1929.png

Math Expert
Joined: 02 Sep 2009
Posts: 52428
Re: In the figure above, the circle with center O has diameter 10 and the  [#permalink]

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02 Dec 2017, 03:25
KS15 wrote:
Bunuel wrote:

In the figure above, the circle with center O has diameter 10 and the circle with center P has diameter 6. If the two circles are tangent to each other, what is the length of the segment OP?

(A) 8
(B) 10
(C) 12
(D) 16
(E) 20

Attachment:
2017-11-16_1929.png

Edited. Thank you.
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Re: In the figure above, the circle with center O has diameter 10 and the &nbs [#permalink] 02 Dec 2017, 03:25
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