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

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Bunuel
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In the figure above, circle O and circle P are tangent to each other. [#permalink] New post   30 Jan 2018, 23:41
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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

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

Show Spoiler
Attachment:
2018-01-31_1040.png



Answer is 7

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] New post   31 Jan 2018, 04:01
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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

Show Spoiler
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.

Correct Answer: Option A.

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In the figure above, circle O and circle P are tangent to each other. [#permalink] New post   01 Feb 2018, 10:48
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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

Show Spoiler
Attachment:
2018-01-31_1040.png

Length of OP: simply add radii lengths. Theory below.
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

Answer A

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.

So we simply find the radius of each circle and add radii lengths.
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Re: In the figure above, circle O and circle P are tangent to each other. [#permalink] New post   02 Feb 2018, 12:07
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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

Show Spoiler
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.

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