GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Feb 2019, 12:51

### GMAT 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

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# Common Mistakes in Geometry Questions - Exercise Question #3

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2597
Common Mistakes in Geometry Questions - Exercise Question #3  [#permalink]

### Show Tags

Updated on: 07 Aug 2018, 05:07
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:22) correct 20% (02:17) wrong based on 386 sessions

### HideShow timer Statistics

Common Mistakes in Geometry Questions - Exercise Question #3

ABC is a triangle inscribed in a circle and one of the sides of the triangle is the diameter of the circle with center O and radius 6 units. If angle ABC>angle BAC>angle ACB and angle OAB = $$60^o$$. Find the length of the line segment BC.

A. 6 units
B. 6$$\sqrt{3}$$ units
C. 7 units
D. 7$$\sqrt{3}$$ units
E. 12 units

Common Mistakes in Geometry are explained in detail in the following post:

Detailed solution will be posted soon.

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 22 Nov 2016, 04:33.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:07, edited 4 times in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2597
Common Mistakes in Geometry Questions - Exercise Question #3  [#permalink]

### Show Tags

Updated on: 07 Aug 2018, 05:10
Note: This questions is related to the article on Common Errors in Geometry

Kindly go through the article once, before solving the question or going through the solution.

Official Solution

Given:

• Triangle ABC is inscribed in a circle.
• One of the sides of triangle ABC is the diameter.
• O is the centre and the radius is 6 units.
• angle ABC>angle BAC>angle ACB.
• angle OAB = $$60^o$$

Working:

ABC is inscribed in a circle, with one of the sides as the diameter.

Thus, we can conclude that ABC must be a right-angled triangle since we know that the diameter subtends an angle of 90 degrees on the circumference.

Also, angle ABC>angle BAC>angle ACB,

Therefore, we can infer angle ABC = $$90^o$$ and AC is the diameter of the circle.

From the above diagram,

We can infer that OBA an equilateral triangle and OBC is an isosceles triangle.

Hence, OB = OA = AB = 6 units.

As triangle ABC is a right-angled triangle,

We can apply Pythagoras Theorem and write:

A$$B^2$$ + B$$C^2$$ = A$$C^2$$

$$6^2$$ + B$$C^2$$ = 1$$2^2$$

B$$C^2$$ = 1$$2^2$$ - $$6^2$$

BC = $$6\sqrt{3}$$

Hence, correct option is B

Thanks,
Saquib
Quant Expert
e-GMAT

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 22 Nov 2016, 10:11.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:10, edited 4 times in total.
Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 989
Location: India
GPA: 3.64
Re: Common Mistakes in Geometry Questions - Exercise Question #3  [#permalink]

### Show Tags

22 Nov 2016, 10:14
Considering triangle with AC as diameter of circle.
Since angle ABC>angle BAC>angle ACB and angle OAB = 60 deg.
angle ABC=90 deg, BAC = 60 deg and ACB = 30 deg.
length of BC = AC cos 30 deg = 12 cos 30 = 6 $$\sqrt{3}$$
_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Manager
Joined: 03 Oct 2013
Posts: 84
Re: Common Mistakes in Geometry Questions - Exercise Question #3  [#permalink]

### Show Tags

22 Nov 2016, 14:05
Triangle inscribed in a circle with one sides as the diameter implies a right angled triangle with the diameter as the hypotenuse

Angle ABC is the greatest therefore angle ABC = 90 degrees

This implies AC is the diameter. Given OAB is 60, therefore angle ACB is 30 degrees.

cos (30) = BC/AC => BC = 12*cos(30) = 6 (\sqrt{3})
_________________

P.S. Don't forget to give Kudos on the left if you like the solution

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2597
Re: Common Mistakes in Geometry Questions - Exercise Question #3  [#permalink]

### Show Tags

27 Nov 2016, 07:51
Hey Everyone,

The official solution has been posted. Kindly go through it and if you have any doubts feel free to post your query.

Thanks,
Saquib
Quant Expert
e-GMAT
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Joined: 12 Feb 2016
Posts: 1
Re: Common Mistakes in Geometry Questions - Exercise Question #3  [#permalink]

### Show Tags

25 Aug 2018, 01:09
What if we take BC as diameter
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2597
Re: Common Mistakes in Geometry Questions - Exercise Question #3  [#permalink]

### Show Tags

25 Aug 2018, 01:18
1
arjit5 wrote:
What if we take BC as diameter

Given that angle ABC has the highest value among all the 3 angles. As the triangle is a right-angled triangle, angle ABC = 90.

Now, if angle ABC = 90, the side opposite to that angle, AC, must be the diameter of the circle. Hence, we cannot assume BC as the diameter.

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Common Mistakes in Geometry Questions - Exercise Question #3   [#permalink] 25 Aug 2018, 01:18
Display posts from previous: Sort by