Last visit was: 20 Nov 2025, 03:33 It is currently 20 Nov 2025, 03:33
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
605-655 Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,463
 [8]
Given Kudos: 99,987
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: 105,408
Kudos: 778,463
 [8]
The radius of circle O below is 8 cm. What is the area of the minor 21 Jul 2021, 06:00
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

58% (01:27) correct 42% (01:44) wrong based on 223 sessions

History

Date
Time
Result
Not Attempted Yet

The radius of circle O below is 8 cm. What is the area of the minor segment? (O is the center of the circle.)

(1) The chord AB subtends an angle greater than 90° at the centre.
(2) \(AB = 8\sqrt{3}\) cm


Show Spoiler
Attachment:
2021-06-25_14-56-55.png
2021-06-25_14-56-55.png [ 9.39 KiB | Viewed 3968 times ]
ShowHide Answer
Official Answer
B
User avatar
TestPrepUnlimited
User avatar
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,224
Own Kudos:
1,111
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,224
Kudos: 1,111
The radius of circle O below is 8 cm. What is the area of the minor Updated on: 28 Jul 2021, 19:34
Originally posted by TestPrepUnlimited on 25 Jul 2021, 05:45.
Last edited by TestPrepUnlimited on 28 Jul 2021, 19:34, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The radius of circle O below is 8 cm. What is the area of the minor segment? (O is the center of the circle.)

(1) The chord AB subtends an angle greater than 90° at the centre.
(2) \(AB = 8\sqrt{3}\) cm

Show more

The radius is 8 cm, so the diameter is 16 cm. The chord is between 0 cm and 16 cm then.

Statement 1:

We need an obtuse angle. If the triangle was a right triangle the chord is would be \(\sqrt{2}\) times the radius of 8, so the chord is at least \(8\sqrt{2}\). We can still adjust the chord so insufficient.

Statement 2:

The triangle created by two radii and the chord has lengths 8-8-\(8\sqrt{3}\) so it is a fixed triangle, thus the area is also fixed. Sufficient.

Ans: B
User avatar
Nitisha03
User avatar
Joined: 24 Jun 2021
Last visit: 08 Oct 2022
Posts: 36
Own Kudos:
20
Given Kudos: 88
Location: India
GMAT 1: 640 Q47 V31
GMAT 1: 640 Q47 V31
Posts: 36
Kudos: 20
The radius of circle O below is 8 cm. What is the area of the minor 27 Jul 2021, 03:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Question language is little confusing...does it mean that radius is below 8cm? I assumed that it meant radius of circle is 8cm.
User avatar
TestPrepUnlimited
User avatar
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,224
Own Kudos:
1,111
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,224
Kudos: 1,111
The radius of circle O below is 8 cm. What is the area of the minor 28 Jul 2021, 19:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nitisha03 yes I read that wrong, thanks for pointing that out!
avatar
Muzaffar55
avatar
Joined: 11 Jun 2021
Last visit: 20 Mar 2022
Posts: 1
Given Kudos: 38
Posts: 1
Kudos: 0
The radius of circle O below is 8 cm. What is the area of the minor 29 Jul 2021, 20:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi @TestPrepLimited,

Could you kindly explain how you got the area of the segment using the second condition? When the angle is unknown. We might be able to calculate the area of the triangle. But without the angle formed at the center we can't find the area right?
avatar
rohitagr999
avatar
Joined: 21 Jul 2021
Last visit: 27 Sep 2021
Posts: 11
Own Kudos:
3
Given Kudos: 112
Posts: 11
Kudos: 3
The radius of circle O below is 8 cm. What is the area of the minor 13 Aug 2021, 01:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Muzaffar55
Hi @TestPrepLimited,

Could you kindly explain how you got the area of the segment using the second condition? When the angle is unknown. We might be able to calculate the area of the triangle. But without the angle formed at the center we can't find the area right?
Show more


Even I have exactly same query.. we can calculate area of Triangle but question is asking area of segment. How can this be computed w/o knowing angles.

Also it is not a 45-45-90 triangle because hypotenuse if 8root 3, had it been 45-45-90 triangle hypotenuse would have been 8root2

please correct if i am wrong
User avatar
Fdambro294
User avatar
Joined: 10 Jul 2019
Last visit: 20 Aug 2025
Posts: 1,350
Own Kudos:
742
 [1]
Given Kudos: 1,656
Posts: 1,350
Kudos: 742
 [1]
The radius of circle O below is 8 cm. What is the area of the minor Updated on: 25 Aug 2022, 08:58
Originally posted by Fdambro294 on 13 Aug 2021, 01:27.
Last edited by Fdambro294 on 25 Aug 2022, 08:58, edited 3 times in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Question asks us to find the area of the minor segment AB:

The major segment area will be that portion of the circle above chord AB that is greater than (1/2) the circle’s area


The minor segment area will be that portion of the circle, as shown, that’s is below chord AB.

We are given the radius = 8

To find the area of minor segment AB below chord AB, we can connect 2 radii to points A and B on the circumference of the circle.

Then, if we knew the exact central angle, we could find the entire sector area sectioned off by A-O-B


Lastly, we could Subtract the Area of the triangle AOB from this sector area ———> leaving the area of minor segment AB

If the Central Angle formed by the 2 radii AO and BO is fixed, then we would have a fixed triangle because we have the length of 2 sides given as 8 and the included angle. The 3rd side length will be determined.


S1: central angle subtended by the chord is the central angle described above formed by the 2 Radii AO and BO

Since the angle is not fixed, the sector area and hence the minor segment area will vary.

Not sufficient.


S2: Chord AB subtends the same Central Angle <AOB as does the minor ARC AB

Since we have the radii AO = BO = 8

—And know we are given the 3rd side of the triangle = 8* sqrt(3)

— thus, the entire triangle is defined ———-> meaning the central angle at <AOB is an exact defined value ———-> which means that sector area AOB is a unique, defined area ———> which means that the minor segment area below Chord AB must be uniquely defined as well


We do not have to calculate this measure. It is enough to know that there must be one unique value for minor segment AB.

B S2 sufficient alone

If you wanted to know the exact calculation for statement 2:

Concept: the perpendicular height drawn from the vertex of an isosceles triangle that is between the two equal sides is a “line of symmetry” for the isosceles triangle.

The perpendicular height drawn from this “apex angle” is such that:

Height = Median = Angle Bisector = Perpendicular Bisector.

We connect the two radii to each endpoint of the chord: OA and OB = 8

From center O, we drop this “line of symmetry” height such that it is perpendicular to the chord. We can call the intersection point X and this height =
OX.

As stated above, OX, drawn perpendicular from the center of the circle to the chord of length 8 * sqrt(3) will BISECT the chord.

AX = XB = 4 * sqrt(3) —— (since point X is the Midpoint of chord AB, i.e., height OX is also the Median)

Height/Median OX will create two right triangles within the isosceles triangle — right triangles AXO and BXO

Within right triangle AXO:

One Leg = 4 * sqrt(3)

Hypotenuse = 8

The ratio of (Leg) to (Hypotenuse) = 4 * sqrt(3) : 8 = sqrt(3) : 2

Only a 30-60-90 right triangle will have THAT Leg-to-Hypotenuse Ratio

Thus, the two right triangles created by height OX are each 30-60-90 right triangles.

Each bisected part of the chord is across from the 60 degree angle. This means, that the central angle AOX = 60 + 60 = 120 degrees ——— (note: height OX is also the angle Bisector of the angle at vertex O)

We can find the entire sector area defined by central angle AOB:
(120/360) * (8)^2 * (pi) =

64(pi) / 3

Then, to find the minor segment area, we subtract out the Area of the Triangle created by the chord AB and the two radii, AO and BO.

According to the ratios of the 30-60-90 right triangles:

Height OX = 4 —— is across from the 30 degree angle
AX = 4 * Sqrt(3) ——- is across from
The 60 degree angle

——> so, the Base = Chord AB = 8 * sqrt(3)

(and the hypotenuse OA = 8)

Area of triangle AXO = (1/2) (4) (8 * sqrt(3)) = 16 * sqrt(3)

Hence, the Area of the minor segment is equal to =

(64pi / 3) — (16 * sqrt(3))

B — s2 is sufficient alone

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,597
Own Kudos:
1,079
Posts: 38,597
Kudos: 1,079
The radius of circle O below is 8 cm. What is the area of the minor 14 Nov 2024, 08:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105408 posts
kingbucky
496 posts