Last visit was: 08 Sep 2026, 04:49 It is currently 08 Sep 2026, 04:49
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
605-655 (Medium)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Sep 2026
Posts: 113,236
Own Kudos:
839,971
 [4]
Given Kudos: 111,380
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,236
Kudos: 839,971
 [4]
A circle is inscribed in an isosceles trapezoid with bases 8 and 18 28 Jun 2023, 00:30
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
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:

63% (02:15) correct 38% (02:59) wrong based on 48 sessions

History

Date
Time
Result
Not Attempted Yet

A circle is inscribed in an isosceles trapezoid with bases 8 and 18 as shown above. What is the area of the circle?

A. \(25\pi\)
B. \(30\pi\)
C. \(36\pi\)
D. \(49\pi\)
E. \(64\pi\)

Show Spoiler
Attachment:
2023-06-28_11-18-47.png
2023-06-28_11-18-47.png [ 6.65 KiB | Viewed 6670 times ]
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 07 Sep 2026
Posts: 7,312
Own Kudos:
17,472
 [5]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 7,312
Kudos: 17,472
 [5]
A circle is inscribed in an isosceles trapezoid with bases 8 and 18 28 Jun 2023, 09:44
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel

A circle is inscribed in an isosceles trapezoid with bases 8 and 18 as shown above. What is the area of the circle?

A. \(25\pi\)
B. \(30\pi\)
C. \(36\pi\)
D. \(49\pi\)
E. \(64\pi\)

Show Spoiler
Attachment:
The attachment 2023-06-28_11-18-47.png is no longer available
Show more

Answer: Option C

Please check teh explanation in attachment
Attachments

Screenshot 2023-06-28 at 10.12.17 PM.png
Screenshot 2023-06-28 at 10.12.17 PM.png [ 1.05 MiB | Viewed 6025 times ]

General Discussion
User avatar
vedha0
User avatar
Joined: 10 Jan 2023
Last visit: 17 Mar 2024
Posts: 120
Own Kudos:
128
 [1]
Given Kudos: 58
Posts: 120
Kudos: 128
 [1]
A circle is inscribed in an isosceles trapezoid with bases 8 and 18 25 Jul 2023, 22:55
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PU = PT = a. but this need not be equal to QV or QU. QV=QU=b. and then RV=RW=c and ST=SW=d

However, since its isoceles trapezoid, PS = QR. so we eventually get PS = QR = 13 on solving using given information. 5-12-13 triplet implies dia is 12 and thus radius is 6. hence, area is 36*pi . so the answer is still C. How is the answer A? Bunuel can you please give OE?

GMATinsight
Bunuel

A circle is inscribed in an isosceles trapezoid with bases 8 and 18 as shown above. What is the area of the circle?

A. \(25\pi\)
B. \(30\pi\)
C. \(36\pi\)
D. \(49\pi\)
E. \(64\pi\)

Show Spoiler
Attachment:
2023-06-28_11-18-47.png

Answer: Option C

Please check teh explanation in attachment
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Sep 2026
Posts: 113,236
Own Kudos:
839,971
 [1]
Given Kudos: 111,380
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,236
Kudos: 839,971
 [1]
A circle is inscribed in an isosceles trapezoid with bases 8 and 18 26 Jul 2023, 01:45
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
vedha0
PU = PT = a. but this need not be equal to QV or QU. QV=QU=b. and then RV=RW=c and ST=SW=d

However, since its isoceles trapezoid, PS = QR. so we eventually get PS = QR = 13 on solving using given information. 5-12-13 triplet implies dia is 12 and thus radius is 6. hence, area is 36*pi . so the answer is still C. How is the answer A? Bunuel can you please give OE?

GMATinsight
Bunuel

A circle is inscribed in an isosceles trapezoid with bases 8 and 18 as shown above. What is the area of the circle?

A. \(25\pi\)
B. \(30\pi\)
C. \(36\pi\)
D. \(49\pi\)
E. \(64\pi\)

Show Spoiler
Attachment:
2023-06-28_11-18-47.png

Answer: Option C

Please check teh explanation in attachment
Show more
_________________________________________
The OA is A, not C. Edited. Thank you for notifying!
User avatar
unraveled
User avatar
Joined: 07 Mar 2019
Last visit: 10 Apr 2025
Posts: 2,696
Own Kudos:
2,405
Given Kudos: 763
Location: India
WE:Sales (Energy)
Posts: 2,696
Kudos: 2,405
A circle is inscribed in an isosceles trapezoid with bases 8 and 18 26 Jul 2023, 09:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post

A circle is inscribed in an isosceles trapezoid with bases 8 and 18 as shown above. What is the area of the circle?

A. \(25\pi\)
B. \(30\pi\)
C. \(36\pi\)
D. \(49\pi\)
E. \(64\pi\)
Area of circle = \(r^2\pi\)
Therefore the answer choice must be a multiple of square of a number(most likely an integer as we see the choice available).
Here itself we can reject B as 30 is not a square of an integer.

Since this is an isosceles trapezoid, the sides non parallel sides are equal. The figure is such that circles fits in such a manner that all sides touch circle uniformly i.e. point of touch divides parallel sides in half and non parallel ones in equal ratios. the smaller part of those non parallel sides is of the length 4(8/2) and bigger one is of the length 9(18/2). Now that we know the length of the non parallel sides is 13(4 + 9) we can get the distance between the tow parallel sides using Pythagoras theorem, which gives us 12. Thus, radius is 6.

Now if we see the answer choices we have only one choice that is a multiple of 6 or 6ˆ2.

Note: the non parallel sides would touch circle such that the point of touch divides them in the ratio of length of parallel sides i.e. 8/18 = 4/9. Actually, here it is 4 and 9.

Answer C.
User avatar
ThatIndianGuy
User avatar
Joined: 18 Mar 2020
Last visit: 09 Apr 2026
Posts: 74
Own Kudos:
65
 [1]
Given Kudos: 385
Location: India
Concentration: Strategy, Technology
Schools: Schulich '27 (A$) IE (A) Bocconi (I) Rotman '27 (A$) IESE '27 (D) ESADE (A)
WE:General Management (Technology)
Schools: Schulich '27 (A$) IE (A) Bocconi (I) Rotman '27 (A$) IESE '27 (D) ESADE (A)
Posts: 74
Kudos: 65
 [1]
A circle is inscribed in an isosceles trapezoid with bases 8 and 18 26 Jul 2023, 10:43
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Tangents drawn to a circle are equal in length.

Therefore,
We take one tangent of 18/2 = 9 and other of 8/2 = 4
Total length of hypotenuse = 9+4 = 13
Base = 5

Height = 12 (Pythagoras)

Radius = 12/2 = 6

Area = 36π
Option C
Attachments

Untitled.png
Untitled.png [ 18.2 KiB | Viewed 5087 times ]

Moderator:
Bunuel
Math Expert
113236 posts