Last visit was: 18 May 2026, 00:23 It is currently 18 May 2026, 00:23
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
505-555 (Easy)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 May 2026
Posts: 110,574
Own Kudos:
815,463
Given Kudos: 106,290
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,574
Kudos: 815,463
In the figure, O is the center of the circle. Which one of the followi 31 Oct 2019, 00:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

74% (01:01) correct 26% (01:03) wrong based on 62 sessions

History

Date
Time
Result
Not Attempted Yet

In the figure, O is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?

(A) Always less than 10
(B) Always greater than 40
(C) Always greater than 30
(D) Always less than 30
(E) Less than 40 and greater than 20

Show Spoiler
Attachment:
circle.jpg
circle.jpg [ 7.85 KiB | Viewed 6166 times ]
ShowHide Answer
Official Answer
E
User avatar
CareerGeek
User avatar
Joined: 20 Jul 2017
Last visit: 17 May 2026
Posts: 1,286
Own Kudos:
4,459
 [1]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
GMAT 1: 690 Q51 V30
Posts: 1,286
Kudos: 4,459
 [1]
In the figure, O is the center of the circle. Which one of the followi 31 Oct 2019, 04:22
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel

In the figure, O is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?

(A) Always less than 10
(B) Always greater than 40
(C) Always greater than 30
(D) Always less than 30
(E) Less than 40 and greater than 20

Show Spoiler
Attachment:
circle.jpg
Show more

Perimeter of triangle OAB = OA + OB + AB = 10 + 10 + AB
= 20 + AB

3rd side property of a triangle:
3rd side is always greater than difference of the other two sides and less than sum of the other two sides
—> AB > 10 - 10
—> AB > 0
and
AB < 10 + 10
—> AB < 20

So, Perimeter is > 20 and < 40

IMO Option E

Posted from my mobile device
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,651
Own Kudos:
21,005
Given Kudos: 165
Expert
Expert reply
Posts: 3,651
Kudos: 21,005
In the figure, O is the center of the circle. Which one of the followi 31 Oct 2019, 05:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post

Solution



Given
• O is the center of the circle as shown.

To find
• The option that is true about the perimeter of the triangle AOB

Approach and Working out
• AO = BO = Radius of the circle = 10
• Difference of other two sides < Third Side < Sum of other two sides
• 10 – 10 < Third side < 10 + 10
• 0 < Third side < 20
• 0 + length of other two sides < length of other two sides + third side < 20 + length of other two sides
• 20 < Perimeter < 40

Thus, option E is the correct answer.
Correct Answer: Option E
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,896
Own Kudos:
5,466
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,896
Kudos: 5,466
In the figure, O is the center of the circle. Which one of the followi 31 Oct 2019, 11:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the figure, O is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?

(A) Always less than 10
(B) Always greater than 40
(C) Always greater than 30
(D) Always less than 30
(E) Less than 40 and greater than 20

Show Spoiler
Attachment:
circle.jpg
Show more
The sum of any 2 sides of a triangle must be greater than the measure of the third side

O is the centre of the triangle , So OA = OB = 10 cm

Now, AB < OB + OA

Or, AB < 10 + 10

Or, AB < 20

Say AB = 19

So, Perimeter of the Tiangle will be 10 +10 + 19 = 39 , Hence Answer must be (E)
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 15 May 2026
Posts: 22,344
Own Kudos:
26,594
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,344
Kudos: 26,594
In the figure, O is the center of the circle. Which one of the followi 03 Nov 2019, 20:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the figure, O is the center of the circle. Which one of the following must be true about the perimeter of the triangle shown?

(A) Always less than 10
(B) Always greater than 40
(C) Always greater than 30
(D) Always less than 30
(E) Less than 40 and greater than 20

Show Spoiler
Attachment:
circle.jpg
Show more


We see that two sides of the triangle, OA and OB, must be 10 each since they are also the radii of the circle. So the 3rd side, AB, must be greater than 0 but less than 20 (the sum of the lengths of OA and OB). Therefore, the perimeter of the triangle must be greater than 10 + 10 + 0 = 20, but less than 10 + 10 + 20 = 40.

Alternate Solution:

Let’s consider the triangle AOB that is formed when A and B are just next to each other, so the distance from A to B is just slightly greater than 0. Then the perimeter of the triangle will be 10 + 10 + (negligible) = slightly greater than 20.

Now consider triangle AOB that is formed when A and B are nearly opposite each other, almost creating a diameter of the circle. In this case, the third side, AB, is nearly 20. In this case, the perimeter of the triangle is 10 + 10 + (almost 20) = just less than 40.

Thus, we see that the perimeter of triangle AOB must be less than 40 and greater than 20.

Answer: E
Moderators:
Bunuel
Math Expert
110574 posts
Krunaal
Tuck School Moderator
852 posts