It is currently 14 Dec 2017, 11:12

# Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1 | UCLA R1

### 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 a square is inscribed in a circle of radius r as shown above, then

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42608

Kudos [?]: 135644 [0], given: 12705

If a square is inscribed in a circle of radius r as shown above, then [#permalink]

### Show Tags

21 Nov 2017, 22:19
00:00

Difficulty:

25% (medium)

Question Stats:

91% (00:46) correct 9% (01:03) wrong based on 34 sessions

### HideShow timer Statistics

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

[Reveal] Spoiler:
Attachment:

2017-11-21_1033.png [ 4.39 KiB | Viewed 460 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135644 [0], given: 12705

Director
Joined: 18 Aug 2016
Posts: 598

Kudos [?]: 181 [0], given: 138

GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If a square is inscribed in a circle of radius r as shown above, then [#permalink]

### Show Tags

21 Nov 2017, 22:32
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

[Reveal] Spoiler:
Attachment:
2017-11-21_1033.png

Diagonal of Square = 2r = $$x\sqrt{2}$$
Area of square = $$(\sqrt{2}r)^2$$
=2r^2

E
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse

Kudos [?]: 181 [0], given: 138

VP
Joined: 22 May 2016
Posts: 1129

Kudos [?]: 402 [0], given: 645

If a square is inscribed in a circle of radius r as shown above, then [#permalink]

### Show Tags

26 Nov 2017, 21:43
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

[Reveal] Spoiler:
Attachment:
2017-11-21_1033.png

Derive side length of square from its diagonal.

Diagonal, d, of square = $$2r$$

Side, s, of square*:

$$s\sqrt{2} = d$$

$$s = \frac{d}{\sqrt{2}}$$

$$s=\frac{2r}{\sqrt{2}}$$ *$$\frac{\sqrt{2}}{\sqrt{2}}$$

$$s= \frac{2r\sqrt{2}}{2}=r\sqrt{2}$$

Area of square = $$s^2$$

A= $$(r\sqrt{2})^2 = 2r^2$$

* derived from
$$s^2 + s^2 = d^2$$
$$2s^2 = d^2$$
$$\sqrt{2}*\sqrt{s^2} = \sqrt{d^2}$$
$$s\sqrt{2} = d$$
$$s = \frac{d}{\sqrt{2}}$$

Kudos [?]: 402 [0], given: 645

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1940

Kudos [?]: 1018 [0], given: 3

Location: United States (CA)
Re: If a square is inscribed in a circle of radius r as shown above, then [#permalink]

### Show Tags

29 Nov 2017, 09:57
Bunuel wrote:

If a square is inscribed in a circle of radius r as shown above, then the area of the square region is

(A) r^2/2π
(B) πr^2/2
(C) πr^2
(D) r^2
(E) 2r^2

[Reveal] Spoiler:
Attachment:
2017-11-21_1033.png

Since the radius is r, the circle’s diameter = diagonal of square = 2r.

Since diagonal = side√2:

2r = side√2

2r/√2 = side

Thus, area of the square = (2r/√2)^2 = 4r^2/2= 2r^2.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1018 [0], given: 3

Re: If a square is inscribed in a circle of radius r as shown above, then   [#permalink] 29 Nov 2017, 09:57
Display posts from previous: Sort by