Last visit was: 18 Jun 2024, 14:28 It is currently 18 Jun 2024, 14:28

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
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [1]
Given Kudos: 25368
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [0]
Given Kudos: 25368
Send PM
avatar
Intern
Intern
Joined: 04 Nov 2023
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [0]
Given Kudos: 25368
Send PM
Re: Triangle ABC is contained within a circle with center C. Points A and [#permalink]
Expert Reply
Here sir the question is not assuming is a perfect triangle. it is a deduction based on the information in the stem
avatar
Intern
Intern
Joined: 04 Nov 2023
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: Triangle ABC is contained within a circle with center C. Points A and [#permalink]
What information in the stem leads us to figuring out it is an equilateral?
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [0]
Given Kudos: 25368
Send PM
Re: Triangle ABC is contained within a circle with center C. Points A and [#permalink]
Expert Reply
We are told that triangle \(ABC\) is contained within a circle with center \(C\) and points \(A\) and \(B\) lie on the circle.

We are also given that area of the circle is \(25\pi\).

We know that area of triangle \(= \pi \times radius^2\). Thus we can say: \(\pi \times radius^2 = 25 \times \pi\)

\(⇒ \pi \times radius^2 = 25 \times \pi\)

\(⇒ radius^2=25\)

\(⇒ radius=\sqrt{25}\)

\(⇒ radius=5\)

We are given that \(\angle ACB = 60^o\)

After all this information, we can draw:

Image


Since \(AC=CB\), the angles opposite to them i.e., \(\angle A\) and \(\angle B\) will also be same

Thus we can say: \(\angle A+\angle B +\angle C = 180^o\)

\(⇒ \angle A + \angle A + 60 = 180\)

\(⇒ 2\times \angle A = 120\)

\(⇒ \angle A = 60^o\)

Thus \(\angle A = \angle B = \angle C = 60^o\)

So, triangle ABC is an equilateral triangle. So the possible value of \(AB = 5\).

Hence the right answer is Option C.
Verbal Expert
Joined: 18 Apr 2015
Posts: 28951
Own Kudos [?]: 33733 [0]
Given Kudos: 25368
Send PM
Re: Triangle ABC is contained within a circle with center C. Points A and [#permalink]
Expert Reply
For all the students above: we have to infer information from the stem NOT always we can assume information from the stem!!!
Prep Club for GRE Bot
[#permalink]
Moderators:
Moderator
1088 posts
GRE Instructor
218 posts

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