Last visit was: 05 Nov 2024, 16:29 It is currently 05 Nov 2024, 16:29

Close

GRE Prep 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
Your Progress

every week, we’ll send you an estimated GRE 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.

Close

Request Expert Reply

Confirm Cancel
User avatar
Director
Director
Joined: 22 Jun 2019
Posts: 521
Own Kudos [?]: 706 [6]
Given Kudos: 161
Send PM
avatar
Active Member
Active Member
Joined: 03 Apr 2019
Posts: 195
Own Kudos [?]: 276 [1]
Given Kudos: 0
Send PM
User avatar
Director
Director
Joined: 22 Jun 2019
Posts: 521
Own Kudos [?]: 706 [0]
Given Kudos: 161
Send PM
avatar
Intern
Intern
Joined: 14 May 2019
Posts: 31
Own Kudos [?]: 53 [1]
Given Kudos: 36
Send PM
Re: Finding ratio from unknown circle. [#permalink]
1
Bookmarks
the base of the equilateral triangle to the center of the small circle=1/3 the height of the triangle
the vertex of any side of the triangle( which touches the circumference of the bigger circle) to the center of the bigger circle (which also coincides with the center of the smaller circle)= 2/3 the height of the triangle
radius of smaller circle=1/3
radius of bigger circle=2/3
small circle area:bigger circle area=(1/3)^2:(2/3)^2=1:4
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [3]
Given Kudos: 136
Send PM
Re: Finding ratio from unknown circle. [#permalink]
3
Here's a similar question to practice with: https://gre.myprepclub.com/forum/in-the-ab ... -9519.html

Cheers,
Brent
User avatar
Director
Director
Joined: 22 Jun 2019
Posts: 521
Own Kudos [?]: 706 [0]
Given Kudos: 161
Send PM
Re: Finding ratio from unknown circle. [#permalink]
1
GreenlightTestPrep wrote:
Here's a similar question to practice with: https://gre.myprepclub.com/forum/in-the-ab ... -9519.html

Cheers,
Brent


Many Many Many Thanks :thanks :-D
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Own Kudos [?]: 3209 [3]
Given Kudos: 172
Location: India
WE:Education (Education)
Send PM
Re: Finding ratio from unknown circle. [#permalink]
3
huda wrote:
Attachment:
What is the ratio of the two circles.png


What is the ratio of the two circles? (Assume that the triangle you see onto the circle is an equilateral triangle).



Enter your answer.

Show: :: OA
1:4


huda
Ratio of two circles what?

Radius: 2:1
Area: 4:1
Circumference: 2:1

[NOTE: All the above ratios are bigger circle to smaller circle]
Manager
Manager
Joined: 16 Aug 2021
Posts: 139
Own Kudos [?]: 46 [0]
Given Kudos: 86
Send PM
Re: Finding ratio from unknown circle. [#permalink]
let S the length of the side of the triangle
so the height will be
H^2 +(S^2/4)=S^2
So H = sqr(3)*S/2
the area of the triangle will be =sqr (3) *S^2 /4
as the small circle attachments to the triangle can divide the area into three equal triangles
so the small triangle will be =sqr (3) *S^2 /12
so the radius of the small circle will be =2*(sqr (3) *S^2 /12)/S
so r = sqr (3)*S/6
so the radius of the big circle will be : height - radius of small
so R =2* sqr (3)*S/6
so the ration will be r to R is 1:4
Intern
Intern
Joined: 08 Aug 2022
Posts: 49
Own Kudos [?]: 36 [0]
Given Kudos: 98
Send PM
Finding ratio from unknown circle. [#permalink]
Assuming they are looking for the ratio of the AREAS of the small circle to the big circle:

1. Draw a line from the center of the small circle to the center of one side of the triangle, such that it creates a 90-degree angle with the side of the triangle. This line is small radius = r. Area of small circle = pi*r^2

2. Draw another line from the center of the circle to one of the corners of the triangle immediately adjacent to the prior line. Since we know we can draw three of each of these types of lines, thus dividing the circle into 6 pie slices, and a circle has 360 degrees total, we now have an angle between these two lines at the center of the circle = 60 degrees. We have now created a 30-6o-90 triangle where the small side = r (as defined above) and the hypotenuse = 2r = the radius of the bigger circle. So the area of the bigger circle = pi * (2r)^2 = 4*pi*r^2.

3. (pi*r^2): (4*pi*r^2) = 1:4
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: Finding ratio from unknown circle. [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
Re: Finding ratio from unknown circle. [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne