Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 22 Jul 2019, 16:26

### 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

# What is the radius of the circle shown above with center O, if CB is a

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56357
What is the radius of the circle shown above with center O, if CB is a  [#permalink]

### Show Tags

24 Aug 2018, 02:46
00:00

Difficulty:

15% (low)

Question Stats:

92% (01:16) correct 8% (01:52) wrong based on 36 sessions

### HideShow timer Statistics

What is the radius of the circle shown above with center O, if CB is a line segment of length 8 that is tangent to the circle and the distance between C and the center of the circle is 10?

A. 4

B. 6

C. $$4\sqrt{3}$$

D. 8

E. $$2\sqrt{41}$$

Attachment:

image033.jpg [ 2.29 KiB | Viewed 526 times ]

_________________
VP
Joined: 31 Oct 2013
Posts: 1394
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
What is the radius of the circle shown above with center O, if CB is a  [#permalink]

### Show Tags

Updated on: 24 Aug 2018, 04:22
Bunuel wrote:

What is the radius of the circle shown above with center O, if CB is a line segment of length 8 that is tangent to the circle and the distance between C and the center of the circle is 10?

A. 4

B. 6

C. $$4\sqrt{3}$$

D. 8

E. $$2\sqrt{41}$$

Attachment:
image033.jpg

CO = 10

CB= 8

BO =?

Applying the Pythagorean Theorem :

$$CO^2 = CB^2 + BO^2$$

$$10^2 = 8^2 + BO^2$$

$$100 - 64 = BO^2$$

$$BO^2 = 36$$

BO = 6.

Originally posted by KSBGC on 24 Aug 2018, 03:11.
Last edited by KSBGC on 24 Aug 2018, 04:22, edited 1 time in total.
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 541
Location: India
Re: What is the radius of the circle shown above with center O, if CB is a  [#permalink]

### Show Tags

24 Aug 2018, 03:16
Hi,

For geometry questions, try to draw the figure and label the information, properties associated with the figure, you will get the answers quickly.

Here they have given a circle and shown tangents whose length is 8. Also given distance between C and centre is 10.

Remember: Tangent and radius are perpendicular to each other.

We can use the right triangle pythogorean rule and get the value of the radius.

Look at the below diagram for better understanding.

Or else, know the common pythogorean triplets 3-4-5, 6-8-10 and 5-12-13. Very popular in aptitude exams.

So here is the radius of the circle is 6.

Attachments

GTC - 24-08-18.png [ 12.01 KiB | Viewed 454 times ]

_________________
GMAT Mentors
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: What is the radius of the circle shown above with center O, if CB is a  [#permalink]

### Show Tags

24 Aug 2018, 03:28
selim wrote:
Bunuel wrote:

What is the radius of the circle shown above with center O, if CB is a line segment of length 8 that is tangent to the circle and the distance between C and the center of the circle is 10?

A. 4

B. 6

C. $$4\sqrt{3}$$

D. 8

E. $$2\sqrt{41}$$

Attachment:
image033.jpg

CO = 10

CB= 8

BO =?

Applying the Pythagorean Theorem :

$$CO^2 = CB^2 + BO^2$$

$$10^2 = 8^2 + BO^2$$

$$100 - 64 = BO^2$$

$$BO^2 = 36$$

BO = 6.

It must be a typo. BO=6 corresponds Ans.B
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
VP
Joined: 31 Oct 2013
Posts: 1394
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: What is the radius of the circle shown above with center O, if CB is a  [#permalink]

### Show Tags

24 Aug 2018, 04:22
PKN wrote:
selim wrote:
Bunuel wrote:

What is the radius of the circle shown above with center O, if CB is a line segment of length 8 that is tangent to the circle and the distance between C and the center of the circle is 10?

A. 4

B. 6

C. $$4\sqrt{3}$$

D. 8

E. $$2\sqrt{41}$$

Attachment:
image033.jpg

CO = 10

CB= 8

BO =?

Applying the Pythagorean Theorem :

$$CO^2 = CB^2 + BO^2$$

$$10^2 = 8^2 + BO^2$$

$$100 - 64 = BO^2$$

$$BO^2 = 36$$

BO = 6.

It must be a typo. BO=6 corresponds Ans.B

Thanks PKN. Edited.
Re: What is the radius of the circle shown above with center O, if CB is a   [#permalink] 24 Aug 2018, 04:22
Display posts from previous: Sort by