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, weโll 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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
An equilateral triangle is inscribed in a circle. If the perimeter of
[#permalink]
06 Sep 2021, 10:00
1
Expert Reply
2
Bookmarks
00:00
Question Stats:
81% (02:40) correct
18% (02:06) wrong based on 16 sessions
HideShow
timer Statistics
An equilateral triangle is inscribed in a circle. If the perimeter of the triangle is z inches and the area of the circle is y square inches, which of the following equations must be true?
An equilateral triangle is inscribed in a circle. If the perimeter of
[#permalink]
30 Nov 2021, 06:25
3
Attachment:
temp-2.JPG [ 30.92 KiB | Viewed 2326 times ]
Side of an equilateral triangle (a) inscribed in a circle with radius r is given by a = rโ๐ [ Watch this video to know how ]
=> Perimeter of triangle = 3a = 3 * โ๐ r = z (given) => r = \(\frac{z }{ 3 โ๐}\)
Area of circle with radius r = \(\pi r^2\) = y (given) => \(\pi\) * \((\frac{z }{ 3 โ๐})^2\) = y (substituting value of r from (1) ) => \(\pi\) * \(\frac{z^2}{9*3}\) = y => \(\pi\) * \(\frac{z^2}{27}\) = y => \(\pi\) * \(z^2\) = 27 * y => \(\pi z^2-27y=0\)
So, Answer will be E Hope it helps!
Watch the following video to Learn Properties of Equilateral Triangle inscribed in a Circle
Re: An equilateral triangle is inscribed in a circle. If the perimeter of
[#permalink]
06 Sep 2021, 17:42
3
Answer is E) pi *z^2โ27y=0
Let s be the side of the triangle and r be the radius of the circle, the relation between them is s = r * sqrt(3). So z = 3 * s = 3*sqrt(3) * r. and area = pi * r^2. All the answer choices are relation between y and z and y already has a pi in it, so in the answer only C,D,E has pi multiplied for z. Next step is simple, relation between z and y in terms of r and E is the only one that satisfies.
PS: Not sure this is the GRE method, please share if there is a shorter approach.
Re: An equilateral triangle is inscribed in a circle. If the perimeter of
[#permalink]
14 Apr 2024, 10:39
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.
gmatclubot
Re: An equilateral triangle is inscribed in a circle. If the perimeter of [#permalink]