• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A circle has center at origin and radius 1...... tagged by: Vincen ##### This topic has 1 expert reply and 0 member replies ## A circle has center at origin and radius 1...... A circle has center at origin and radius 1. The points X, Y, and Z lie on the circle such that the length of arc XYZ is (2/3)Ï€.What is the length of line segment XZ? A. âˆš2 B. âˆš3 C. 2 D. 2+âˆš3 E. 2+âˆš2 The OA is the option B. How can I solve this PS question? I don't know how to find the length of XZ? Experts, could you help me? Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: A circle has center at origin and radius 1. The points X, Y, and Z lie on the circle such that the length of arc XYZ is (2/3)Ï€.What is the length of line segment XZ? A. âˆš2 B. âˆš3 C. 2 D. 2+âˆš3 E. 2+âˆš2 The OA is the option B. How can I solve this PS question? I don't know how to find the length of XZ? Experts, could you help me? Thanks. Hi Vincen, Let's take a look at your question. Center of the circle is (0, 0). Radius = 1 We will use the angle XOZ first using the arc length formula. $$S=\ r\left(theta\right)$$ $$\frac{2\pi}{3}=1\left(theta\right)$$ $$theta=\frac{2\pi}{3}$$ Now we can find the length of XZ using cosine formula in triangle XOZ. The cosine formula is: $$a^2=b^2+c^2-2bc\ Cos\left(A\right)$$ Where A is the angle opposite to the side length a and between the sides b and c. $$\left(XZ\right)^2=\left(1\right)^2+\left(1\right)^2-2\left(1\right)\left(1\right)Cos\left(\frac{2\pi}{3}\right)$$ $$\left(XZ\right)^2=1+1-2\left(-\frac{1}{2}\right)$$ $$\left(XZ\right)^2=2+1$$ $$\left(XZ\right)^2=3$$ $$XZ=\sqrt{3}$$ Therefore, option B is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 68 first replies
2 fskilnik@GMATH 56 first replies
3 Jay@ManhattanReview 39 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

130 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

101 posts
3 Max@Math Revolution

Math Revolution

84 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

79 posts
5 Jay@ManhattanReview

Manhattan Review

76 posts
See More Top Beat The GMAT Experts