GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 06:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58332
In the figure above, circle O and circle P are tangent to each other.  [#permalink]

### Show Tags

30 Jan 2018, 23:41
00:00

Difficulty:

15% (low)

Question Stats:

97% (00:26) correct 3% (00:13) wrong based on 40 sessions

### HideShow timer Statistics

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 984 times ]

_________________
Intern
Joined: 04 Jan 2018
Posts: 37
Re: In the figure above, circle O and circle P are tangent to each other.  [#permalink]

### Show Tags

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
_________________
Don't stop till you get enough

Hit kudos if it helped you.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Re: In the figure above, circle O and circle P are tangent to each other.  [#permalink]

### Show Tags

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.

Thanks,
Saquib Hasnain
Quant Expert
e-GMAT
_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3545
In the figure above, circle O and circle P are tangent to each other.  [#permalink]

### Show Tags

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.

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Choose life.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: In the figure above, circle O and circle P are tangent to each other.  [#permalink]

### Show Tags

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: In the figure above, circle O and circle P are tangent to each other.   [#permalink] 02 Feb 2018, 12:07
Display posts from previous: Sort by