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

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Math Expert
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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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Difficulty:

25% (medium)

Question Stats:

96% (00:19) correct 4% (01:25) wrong based on 48 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

[Reveal] Spoiler:
Attachment:

2017-11-16_1929.png [ 5.7 KiB | Viewed 712 times ]
[Reveal] Spoiler: OA

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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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Untitled1.png [ 9.13 KiB | Viewed 384 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, 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

[Reveal] Spoiler:
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
KUDOS
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

[Reveal] Spoiler:
Attachment:
2017-11-16_1929.png

Kudos [?]: 53 [1], given: 506

Math Expert
Joined: 02 Sep 2009
Posts: 42605

Kudos [?]: 135629 [0], given: 12705

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

[Reveal] Spoiler:
Attachment:
2017-11-16_1929.png

Edited. Thank you.
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Kudos [?]: 135629 [0], given: 12705

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