$O$ is the center of the semicircle. If angle $BCO = 30$ and $BC =6\sqrt3,$ what is the area of triangle $ABO?$

Expert replies

Previous Topic Next Topic

Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun Apr 26, 2020 12:01 pm

Timer

00:00

Answers

Stats

Difficulty—

$O$ is the center of the semicircle. If angle $BCO = 30$ and $BC =6\sqrt3,$ what is the area of triangle $ABO?$

A. $4\sqrt3$
B. $6\sqrt3$
C. $9\sqrt3$
D. $12\sqrt3$
E. $24\sqrt3$

[spoiler]OA=C[/spoiler]

Source: Magoosh

Like this post

Source: Beat The GMAT — Problem Solving | Sun Apr 26, 2020 12:01 pm

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: $O$ is the center of the semicircle. If angle $BCO = 30$ and $BC =6\sqrt3,$ what is the area of triangle \(ABO

by Scott@TargetTestPrep » Sun May 03, 2020 5:27 am

Gmat_mission wrote: ↑
Sun Apr 26, 2020 12:01 pm
triacirc_q1.png

$O$ is the center of the semicircle. If angle $BCO = 30$ and $BC =6\sqrt3,$ what is the area of triangle $ABO?$

A. $4\sqrt3$
B. $6\sqrt3$
C. $9\sqrt3$
D. $12\sqrt3$
E. $24\sqrt3$

[spoiler]OA=C[/spoiler]

Source: Magoosh

Since triangle ABC is inscribed in a semicircle, it’s a right triangle. Since angle BCO is 30 degrees, triangle ABC is a 30-60-90 right triangle. Since BC = 6√3, AB = 6. Thus, the area of triangle ABC = ½ x 6√3 x 6 = 18√3.

Notice that radius BO splits triangle ABC into two smaller triangles: ABO and CBO. Both of these triangles have equal bases (notice AO = CO since they are both radii of the semicircle), and they also have the same height (which can be dropped from point B to AC). Therefore, triangles ABO and CBO have the same area. Since their combined area is the area of triangle ABC, the area of triangle ABO is half that of triangle ABC. Thus, the area of triangle ABO is ½ x 18√3 = 9√3.

Answer: C.

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 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