GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2018, 22:42

### 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 area of the largest circle that can be inscribed in a semi

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50078
What is the area of the largest circle that can be inscribed in a semi  [#permalink]

### Show Tags

21 Nov 2017, 23:29
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:11) correct 13% (00:55) wrong based on 32 sessions

### HideShow timer Statistics

What is the area of the largest circle that can be inscribed in a semicircular region of radius r?

(A) πr^2/4
(B) πr^2/3
(C) πr^2/2
(D) 2πr^2/3
(E) 3πr^2/4

_________________
Manager
Joined: 05 Dec 2016
Posts: 245
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: What is the area of the largest circle that can be inscribed in a semi  [#permalink]

### Show Tags

22 Nov 2017, 00:33
The largest circle would be the circle with diameter=r, hence are of that circle would be P*(1/2*r)^2=p*r^2/4
Intern
Joined: 29 Aug 2016
Posts: 33
Re: What is the area of the largest circle that can be inscribed in a semi  [#permalink]

### Show Tags

22 Nov 2017, 03:04

Max possible diameter of new circle is r. Hence area is pi*d^2.

Sent from my iPhone using GMAT Club Forum
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: What is the area of the largest circle that can be inscribed in a semi  [#permalink]

### Show Tags

27 Nov 2017, 12:34
Bunuel wrote:
What is the area of the largest circle that can be inscribed in a semicircular region of radius r?

(A) πr^2/4
(B) πr^2/3
(C) πr^2/2
(D) 2πr^2/3
(E) 3πr^2/4

The largest circle that can be inscribed in a semicircular region of radius r is one with diameter = radius of the semicircle. In other words, the inscribed circle has a radius that is half of the radius of the circumscribed semicircle. Since the radius of the semicircle = r, the radius of the circle = r/2 and the area of the circle is:

π(r/2)^2 = π(r^2/4)

_________________

Jeffery Miller

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

Re: What is the area of the largest circle that can be inscribed in a semi &nbs [#permalink] 27 Nov 2017, 12:34
Display posts from previous: Sort by