It is currently 22 Mar 2018, 18:36

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If ABC is a quarter circle and a circle is inscribed in it and if AB=

Author Message
TAGS:

Hide Tags

Manager
Joined: 19 Aug 2009
Posts: 78
If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

02 Oct 2009, 09:47
2
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:24) correct 44% (01:55) wrong based on 27 sessions

HideShow timer Statistics

If ABC is a quarter circle and a circle is inscribed in it and if AB= 1 cm, find radius of inner circle.

A. $$\sqrt{2}- 1$$

B. $$\frac{\sqrt{2}+1}{2}$$

C. $$\frac{\sqrt{2}- 1}{2}$$

[Reveal] Spoiler:
Attachment:

GEOMETRY 6.JPG [ 9.99 KiB | Viewed 3095 times ]
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 44400
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

04 Oct 2009, 16:24

If ABC is a quarter circle and a circle is inscribed in it and if AB= 1 cm, find radius of inner circle.

A. $$\sqrt{2}- 1$$

B. $$\frac{\sqrt{2}+1}{2}$$

C. $$\frac{\sqrt{2}- 1}{2}$$

Diagonal of a square made of $$r=r*\sqrt{2}$$

$$R=1= r*\sqrt{2}+r$$ --> $$r=\frac{1}{(\sqrt{2}+1)}=\sqrt{2}-1$$

_________________
Director
Joined: 23 Apr 2010
Posts: 559
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

01 Nov 2010, 03:03
Bunuel, could you please explain this:

Quote:
R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1
Retired Moderator
Joined: 03 Aug 2010
Posts: 227
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

24 Dec 2010, 08:59
Bunuel wrote:

Diagonal of a square made of r=r*\sqrt{2}

R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1

A.

Colud not understand this.. can someone help ?

_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Math Expert
Joined: 02 Sep 2009
Posts: 44400
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

24 Dec 2010, 09:22
3
KUDOS
Expert's post
nonameee wrote:
Bunuel, could you please explain this:

Quote:
R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1

hirendhanak wrote:
Bunuel wrote:

Diagonal of a square made of r=r*\sqrt{2}

R=1= r*\sqrt{2}+r --> r=1/(\sqrt{2}+1)=2^1/2-1

A.

Colud not understand this.. can someone help ?

Look at the diagram:
Attachment:

GEOMETRY 6.PNG [ 11.76 KiB | Viewed 2402 times ]
Diagonal BO of the square made by the radii of the small circle equals to $$BO=\sqrt{r^2+r^2}=r*\sqrt{2}$$;

Now, the radius of the big circle BD equals to $$BO+OD=r*\sqrt{2}+r=1$$ --> $$r=\frac{1}{\sqrt{2}+1}=\sqrt{2}-1$$

_________________
Senior Manager
Joined: 25 May 2010
Posts: 313
Location: United States
Concentration: Strategy, Finance
Schools: CBS '14 (A)
GMAT 1: 590 Q47 V25
GMAT 2: 560 Q47 V20
GMAT 3: 600 Q47 V25
GMAT 4: 680 Q49 V34
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

25 Dec 2010, 10:35
Nice explanation.
_________________

"Whether You Think You Can or Can't, You're Right"--Henry Ford
680 Debrief
600 Debrief
590 Debrief
My GMAT Journey

Manager
Joined: 27 Jul 2010
Posts: 183
Location: Prague
Schools: University of Economics Prague
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

25 Dec 2010, 16:53
Oh this one was tough.
_________________

You want somethin', go get it. Period!

Non-Human User
Joined: 09 Sep 2013
Posts: 6540
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB= [#permalink]

Show Tags

12 Sep 2017, 02:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If ABC is a quarter circle and a circle is inscribed in it and if AB=   [#permalink] 12 Sep 2017, 02:36
Display posts from previous: Sort by