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# In the figure above, circle O and circle P are tangent to each other.

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Joined: 02 Sep 2009
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In the figure above, circle O and circle P are tangent to each other.  [#permalink]

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30 Jan 2018, 23:41
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Difficulty:

15% (low)

Question Stats:

97% (00:18) correct 3% (00:13) wrong based on 37 sessions

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In the figure above, circle O and circle P are tangent to each other. If the circle with center O has a diameter of 8 and the circle with center P has a diameter of 6, what is the length of OP?

(A) 7
(B) 10
(C) 14
(D) 20
(E) 28

Attachment:

2018-01-31_1040.png [ 7.15 KiB | Viewed 712 times ]

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Re: In the figure above, circle O and circle P are tangent to each other.  [#permalink]

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31 Jan 2018, 00:27
Bunuel wrote:

In the figure above, circle O and circle P are tangent to each other. If the circle with center O has a diameter of 8 and the circle with center P has a diameter of 6, what is the length of OP?

(A) 7
(B) 10
(C) 14
(D) 20
(E) 28

Attachment:
2018-01-31_1040.png

Let the point of intersection of 2 circles be M
radius of circle O= OM = 4
radius of circle P =MP= 3
OP= OM+MP= 7
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Re: In the figure above, circle O and circle P are tangent to each other.  [#permalink]

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31 Jan 2018, 04:01
Bunuel wrote:

In the figure above, circle O and circle P are tangent to each other. If the circle with center O has a diameter of 8 and the circle with center P has a diameter of 6, what is the length of OP?

(A) 7
(B) 10
(C) 14
(D) 20
(E) 28

Attachment:
2018-01-31_1040.png

Solution

• Let the point at which the two circles touch each be X.

• We need to find the value of $$OP = OX + PX$$

• From the diagram it is evident that OX and PX are the radius of the two circles with center O and P respectively.

o Since diameter of circle with center O is $$8$$, its radius will be $$= \frac{8}{2} = 4$$ units

o And since the diameter of circle with center P is 6, its radius will be $$= \frac{6}{2} = 3$$ units

• Thus, the length of $$OP = OX + PX = 4 + 3 = 7$$ units.

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Saquib Hasnain
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In the figure above, circle O and circle P are tangent to each other.  [#permalink]

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01 Feb 2018, 10:48
Bunuel wrote:

In the figure above, circle O and circle P are tangent to each other. If the circle with center O has a diameter of 8 and the circle with center P has a diameter of 6, what is the length of OP?

(A) 7
(B) 10
(C) 14
(D) 20
(E) 28

Attachment:
2018-01-31_1040.png

Diameter of a circle = 2r
Radius of Circle O = 4 (d=8, 8/2 = 4)
Radius of Circle P = 3 (d=6, 6/2 = 3)

3 + 4 = 7

Theory: If two circles are tangent to each other, then the circles touch at exactly one point. Further, any line that is tangent to a circle is perpendicular to the circle's radius.

In this case, the common tangent line is perpendicular to both circles' radii at the point of tangency -- which means that the tangent point and the two centers lie on the same line. Each radius is a segment on the same line.

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Re: In the figure above, circle O and circle P are tangent to each other.  [#permalink]

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02 Feb 2018, 12:07
Bunuel wrote:

In the figure above, circle O and circle P are tangent to each other. If the circle with center O has a diameter of 8 and the circle with center P has a diameter of 6, what is the length of OP?

(A) 7
(B) 10
(C) 14
(D) 20
(E) 28

Attachment:
2018-01-31_1040.png

Since the circle with center O has a diameter of 8 and the circle with center P has a diameter of 6, the radius of circle O is 4, and the radius of circle P is 3, so OP = 4 + 3 = 7.

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Re: In the figure above, circle O and circle P are tangent to each other. &nbs [#permalink] 02 Feb 2018, 12:07
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