GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Feb 2020, 02:13 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A circle, with center O, is inscribed in square WXYZ. Point P, as

Author Message
TAGS:

### Hide Tags

Manager  Joined: 09 Oct 2008
Posts: 83
A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

9 00:00

Difficulty:   95% (hard)

Question Stats: 44% (02:42) correct 56% (02:29) wrong based on 135 sessions

### HideShow timer Statistics A circle, with center O, is inscribed in square WXYZ. Point P, as shown above, is where the circle and the line segment ZX intersect. If PX = 1, which of the following is closest to the value of the circumference of the circle?

A. 2π
B. 3π
C. 4π
D. 5π
E. 6π

Attachment: Picture2-1%5B1%5D.png [ 10.55 KiB | Viewed 7377 times ]

Originally posted by vishalgc on 09 Oct 2008, 20:34.
Last edited by Bunuel on 13 Jun 2015, 09:35, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Math Expert V
Joined: 02 Sep 2009
Posts: 61385
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

5
1
petu wrote:
Hi, could someone give help me with this one? I just can't understand the explanations! thanks!!! A circle, with center O, is inscribed in square WXYZ. Point P, as shown above, is where the circle and the line segment ZX intersect. If PX = 1, which of the following is closest to the value of the circumference of the circle?

A. 2π
B. 3π
C. 4π
D. 5π
E. 6π

Check image below: Notice that triangle AOX is an isosceles right triangle: AO = AX = radius.

We know that hypotenuse of an isosceles right triangle is $$side*\sqrt{2}$$, thus = $$OX=side*\sqrt{2}=radius*\sqrt{2}$$.

On the other hand, OX = OP + PX = radius + PX = radius + 1.

Therefore, $$radius + 1=radius*\sqrt{2}$$:

$$radius=\frac{1}{\sqrt{2}-1}=\sqrt{2}+1\approx{1.4+1}=2.4$$.

The circumference = $$2\pi{r}=2\pi*2.4=4.8\pi$$.

Hope it's clear.
Attachment: Untitled.png [ 7.12 KiB | Viewed 7292 times ]

_________________
##### General Discussion
VP  Joined: 17 Jun 2008
Posts: 1023
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

1
5pi.

OX = OP + 1 = r + 1 (r is the radius of circle).

Now, OX^2 = r^2 +r^2

Solve for r and then 2pi4 will be approx 5pi.
Manager  Joined: 21 Apr 2008
Posts: 200
Location: Motortown
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

scthakur wrote:
5pi.

OX = OP + 1 = r + 1 (r is the radius of circle).

Now, OX^2 = r^2 +r^2

Solve for r and then 2pi4 will be approx 5pi.

5pi

Yours is a simple way to solve the problem I added unnecessary steps to it Manager  Joined: 15 Apr 2008
Posts: 119
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

scthakur wrote:
5pi.

OX = OP + 1 = r + 1 (r is the radius of circle).

Now, OX^2 = r^2 +r^2

Solve for r and then 2pi4 will be approx 5pi.

can you pls explain why you did OX^2=r^2+r^2
Director  Joined: 30 Jun 2008
Posts: 797
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

scthakur wrote:
5pi.

OX = OP + 1 = r + 1 (r is the radius of circle).

Now, OX^2 = r^2 +r^2

Solve for r and then 2pi4 will be approx 5pi.

Ahhh!! I was not able to see this I was stumped by the question !!

Originally posted by amitdgr on 16 Oct 2008, 18:43.
Last edited by amitdgr on 16 Oct 2008, 18:44, edited 1 time in total.
Current Student Joined: 28 Dec 2004
Posts: 2449
Location: New York City
Schools: Wharton'11 HBS'12
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

let OP=r the radius, then we know that OP+1=OX

or r+1=OX, lets look at the diagonal of the square ZX, ZX=2OX or 2(r+1)

we also know that ZX=sqrt(2)XY; XY=2R...right..with me???

2r+2=sqrt(2)2r

solve for r, you get r=1/(sqrt(2)-1) or 1/0.41

circum. =2pi*r, 2/0.41 is apprx 5...so circum=5pi
VP  Joined: 17 Jun 2008
Posts: 1023
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

ALD wrote:
scthakur wrote:
5pi.

OX = OP + 1 = r + 1 (r is the radius of circle).

Now, OX^2 = r^2 +r^2

Solve for r and then 2pi4 will be approx 5pi.

can you pls explain why you did OX^2=r^2+r^2

The distance between mid-point of XY and O is r and distance between mid-point of XY and X is r. That is why, r^2 + r^2 = OX^2.
Intern  Joined: 30 Mar 2015
Posts: 14
GMAT 1: 730 Q49 V40
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

Hi, could someone give help me with this one? I just can't understand the explanations! thanks!!!
Intern  Joined: 30 Mar 2015
Posts: 14
GMAT 1: 730 Q49 V40
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

THanks Bunuel. Clear as allways. You have few beers waiting for you if you ever come to Barcelona.
Intern  Joined: 04 Jan 2017
Posts: 11
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

That was an excellent explanation. Thanks Brunel!
Intern  Joined: 04 Jan 2017
Posts: 11
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

Sorry to ask what might be an obvious questions.
From your explanation, I don´t understand the part in bold.

Thanks

Check image below:

Image

Notice that triangle AOX is an isosceles right triangle: AO = AX = radius.

We know that hypotenuse of an isosceles right triangle is side∗2‾√side∗2, thus = OX=side∗2‾√=radius∗2‾√OX=side∗2=radius∗2.

On the other hand, OX = OP + PX = radius + PX = radius + 1.

12−1=2+1≈1.4+1=2.4.

The circumference = 2πr=2π∗2.4=4.8π2πr=2π∗2.4=4.8π.

Math Expert V
Joined: 02 Sep 2009
Posts: 61385
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

lauramo wrote:
Sorry to ask what might be an obvious questions.
From your explanation, I don´t understand the part in bold.

Thanks

Check image below:

Image

Notice that triangle AOX is an isosceles right triangle: AO = AX = radius.

We know that hypotenuse of an isosceles right triangle is side∗2‾√side∗2, thus = OX=side∗2‾√=radius∗2‾√OX=side∗2=radius∗2.

On the other hand, OX = OP + PX = radius + PX = radius + 1.

12−1=2+1≈1.4+1=2.4.

The circumference = 2πr=2π∗2.4=4.8π2πr=2π∗2.4=4.8π.

We are solving for radius (you can denote it as x for simplicity) the following equation: $$radius + 1=radius*\sqrt{2}$$ to get $$radius=\frac{1}{\sqrt{2}-1}=\sqrt{2}+1\approx{1.4+1}=2.4$$.

$$x + 1=x*\sqrt{2}$$

$$1=x*\sqrt{2}-x$$

$$1=x(\sqrt{2}-1)$$

$$x=\frac{1}{\sqrt{2}-1}$$

Multiply both numerator and denominator by $$\sqrt{2}+1$$:

$$x=\frac{\sqrt{2}+1}{(\sqrt{2}-1)(\sqrt{2}+1)}=\sqrt{2}+1$$.

Hope it's clear.
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 14119
Re: A circle, with center O, is inscribed in square WXYZ. Point P, as  [#permalink]

### Show Tags

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: A circle, with center O, is inscribed in square WXYZ. Point P, as   [#permalink] 02 Jan 2020, 01:24
Display posts from previous: Sort by

# A circle, with center O, is inscribed in square WXYZ. Point P, as  