• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

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 • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

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

• 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

## Right triangle DEF has angles in the ratio 1:2:3 and is . .

tagged by: VJesus12

This topic has 1 expert reply and 0 member replies

### Top Member

VJesus12 Master | Next Rank: 500 Posts
Joined
14 Oct 2017
Posted:
368 messages
Followed by:
3 members

#### Right triangle DEF has angles in the ratio 1:2:3 and is . .

Thu Nov 30, 2017 9:39 am
Right triangle DEF has angles in the ratio 1:2:3 and is inscribed in a circle with center C such that each vertex of DEF lies on the circumference of C. If the shortest side of DEF has length x, which of the following represents the area of circle C?

A. 2πx

B. πx^2

C. sq. root 3πx^2

D. 2πx^2

E. 4 πx^2

The OA is B .

I don't know how can I solve this PS question. Experts, can you give me some help please? Thanks in advance.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9604 messages
Followed by:
482 members
2867
GMAT Score:
800
Thu Nov 30, 2017 10:52 am
Hi VJesus12,

We're told that Right triangle DEF has angles in the ratio 1:2:3 and is inscribed in a circle with center C such that each vertex of DEF lies on the circumference of C. We're also told that the shortest side of DEF has length X. We're asked which of the following represents the area of circle C. This question is based on a few Geometry rules.

First, the only type of triangle that has angles in the ratio of 1:2:3 is a 30/60/90 right triangle.
Second, for a right triangle to be inscribed in a circle as described, the HYPOTENUSE of the right triangle will be the DIAMETER of the circle.
The ratio of the short side to the long side of a 30/60/90 is 1:2, so the hypotenuse of the right triangle triangle is equal to 2 radii (which is also the length of the short side - X).
Thus, the area of the circle is (pi)(X^2).

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### Top First Responders*

1 GMATGuruNY 103 first replies
2 Brent@GMATPrepNow 43 first replies
3 Rich.C@EMPOWERgma... 34 first replies
4 Jay@ManhattanReview 29 first replies
5 Scott@TargetTestPrep 11 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

152 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

139 posts
3 Scott@TargetTestPrep

Target Test Prep

104 posts
4 Max@Math Revolution

Math Revolution

86 posts
5 Rich.C@EMPOWERgma...

EMPOWERgmat

86 posts
See More Top Beat The GMAT Experts