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

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Bunuel
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In the figure above, the circle with center O has diameter 10 and the [#permalink] New post   16 Nov 2017, 08:30
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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


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A
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KS15
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Re: In the figure above, the circle with center O has diameter 10 and the [#permalink] New post   02 Dec 2017, 03:07
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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


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Attachment:
2017-11-16_1929.png



Bunuel-please correct the answer-it should be A.
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Re: In the figure above, the circle with center O has diameter 10 and the [#permalink] New post   16 Nov 2017, 08:55
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] New post   16 Nov 2017, 08:55
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] New post   16 Nov 2017, 09:32
\(\frac{10+6}{2} = 8\)

Answer will be (A)
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Re: In the figure above, the circle with center O has diameter 10 and the [#permalink] New post   16 Nov 2017, 09:51
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] New post   16 Nov 2017, 13:05
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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


Show 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
Circle O radius = 5
Circle P radius = 3
OP = (3+5) = 8

Answer A
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Re: In the figure above, the circle with center O has diameter 10 and the [#permalink] New post   17 Nov 2017, 14:26
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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.

Answer: A
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Re: In the figure above, the circle with center O has diameter 10 and the [#permalink] New post   02 Dec 2017, 04:25
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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


Show Spoiler
Attachment:
2017-11-16_1929.png



Bunuel-please correct the answer-it should be A.


Edited. Thank you.
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Re: In the figure above, the circle with center O has diameter 10 and the [#permalink]
02 Dec 2017, 04:25
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