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

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Math Expert
Joined: 02 Sep 2009
Posts: 51071
What is the radius of the circle shown above with center O, if CB is a  [#permalink]

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24 Aug 2018, 01:46
00:00

Difficulty:

5% (low)

Question Stats:

94% (00:54) correct 6% (01:14) wrong based on 33 sessions

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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 440 times ]

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Concentration: Accounting, Finance
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WE: Analyst (Accounting)
What is the radius of the circle shown above with center O, if CB is a  [#permalink]

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Updated on: 24 Aug 2018, 03:22
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.

The best answer is B.

Originally posted by selim on 24 Aug 2018, 02:11.
Last edited by selim on 24 Aug 2018, 03:22, edited 1 time in total.
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Re: What is the radius of the circle shown above with center O, if CB is a  [#permalink]

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24 Aug 2018, 02:16
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.

So the answer is B.
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GTC - 24-08-18.png [ 12.01 KiB | Viewed 370 times ]

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Re: What is the radius of the circle shown above with center O, if CB is a  [#permalink]

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24 Aug 2018, 02:28
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.

The best answer is A.

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

PKN

Rise above the storm, you will find the sunshine

Director
Joined: 31 Oct 2013
Posts: 844
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]

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24 Aug 2018, 03:22
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.

The best answer is A.

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 &nbs [#permalink] 24 Aug 2018, 03:22
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# What is the radius of the circle shown above with center O, if CB is a

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