ps - triangle in a circle from GMAT Prep Test - The Beat The GMAT Forum

ps - triangle in a circle from GMAT Prep Test

Expert replies

ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Tue Jun 07, 2011 9:02 am

https://www.beatthegmat.com/area-of-tria ... tml#187497

This question has been discussed but there are differing opinions on what angle in the triangle is 90 degrees and therefore, what the hypot represents. Can anyone clarify? The link is above.

Thanks,

Q. In the figure above, the radius of the circle with the center O is 1 and Bc=1. What is the area of triangular region ABC?

a. root2/2
b. roog3/2
c. 1
d. root2
e. root3

Answer is b

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jun 07, 2011 9:02 am

jainnikhil02: Master | Next Rank: 500 Posts; Posts: 123; Joined: Tue May 31, 2011 12:26 amFollowed by: 1 member; Location: Hyderabad; Thanked: 5 times

by jainnikhil02 » Tue Jun 07, 2011 9:10 am

given that radius =1
so Hypo =2 (diameter in the figure)

so the remaining AB =root3

then area of traingle will be = 1/2 length*breadth
= 1/2*1*root3

=root3/2

Nikhil K Jain
____________________

"Life is all about timing" Don't waste your and others time.

Like this post

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Jun 07, 2011 9:11 am

Hi,
There should be no conflict in opinions. The angle opposite to the diameter is always 90 degrees.
AC = 2, BC=1.
As AC^2 = AB^2 + BC^2, BC = sqrt(3).
Area of triangle is (1/2).AB.BC = (root3)/2

Hence, B

Cheers!

Things are not what they appear to be... nor are they otherwise

Like this post

ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Tue Jun 07, 2011 9:16 am

That is what I thought. Some previous posts were confusing the PT for 1:1:root3, illogically comming to the, coincidentally, correct conclusion. However, as stated the correct PT ratio is 1:root3:2 based on the given information.

Thanks.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 07, 2011 9:33 am

ccassel wrote:That is what I thought. Some previous posts were confusing the PT for 1:1:root3, illogically comming to the, coincidentally, correct conclusion. However, as stated the correct PT ratio is 1:root3:2 based on the given information.

Thanks.

A central angle is formed by two radii.
An inscribed angle is formed by two chords.
When an inscribed angle intercepts the same arc as a central angle, the inscribed angle = 1/2 * the central angle.

Since a diameter is formed by two radii, a diameter is a central angle. The degree measurement of this central angle is 180.
When an inscribed angle intercepts the endpoints of a diameter, it intercepts the same arc on the circle as does the diameter/central angle.
Thus, the degree measurement of the inscribed angle = (1/2)*180 = 90:

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Tue Jun 07, 2011 10:07 pm

AC is the diameter. Also diameters subtend 90 degree angle at the circle.
Thus <ABC is 90
And AC is hypotenuse. AC=2, BC=1
AB^2 = 4-1=3
AB=root(3)
Thus area = (1/2)AB*BC = root(3)/2
IMO B

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
[email protected]

Cans!!

Like this post

kruthika: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Mon Mar 21, 2011 8:39 amFollowed by: 3 members; Location: Chennai; Thanked: 1 times

by kruthika » Tue Jun 07, 2011 11:01 pm

Given that AC is the diameter, and angle subtended in a semicircle is a right angle, therefore <ABC = 90.
Using Pythogoras theorem, we get AB=square root of 3.
Area of a triangle = 1/2 * base * height = 1/2*1*square root of 3 = (square root of 3)/2

Regards,
Kruthika

https://thembaodyssey.blocked/

Like this post

MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Wed Jun 08, 2011 9:26 am

BC radius = 1 so AC = 2

Triangle ratio 30:60:90

so AB = root 3

area = 1/2 root 3 * 1 = root 3/2

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review