Last visit was: 14 Sep 2026, 06:45 It is currently 14 Sep 2026, 06:45
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
705-805 (Hard)|   Geometry|      
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 12 Mar 2026
Posts: 1,840
Own Kudos:
8,794
 [8]
Given Kudos: 707
Location: India
Posts: 1,840
Kudos: 8,794
 [8]
In the given figure AB is the diameter of the circle, whose center is 27 Nov 2019, 08:53
Kudos
Add Kudos
8
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:

75% (hard)

Question Stats:

55% (03:02) correct 45% (02:36) wrong based on 53 sessions

History

Date
Time
Result
Not Attempted Yet
In the given figure AB is the diameter of the circle, whose center is O. Point C lies inside the circle such that ∠ACB=120 degrees. Also, OD is perpendicular to BC and length of OD is 1.5 cm. Find the length of AC?

A. \(\frac{3\sqrt{3}}{2}\)
B. 3
C. \(2\sqrt{3}\)
D. \(3\sqrt{3}\)
E. 6
ShowHide Answer
Official Answer
C

Attachments

Untitled.png
Untitled.png [ 5.34 KiB | Viewed 4154 times ]

User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 13 Sep 2026
Posts: 11,293
Own Kudos:
46,163
 [4]
Given Kudos: 339
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,293
Kudos: 46,163
 [4]
In the given figure AB is the diameter of the circle, whose center is 27 Nov 2019, 21:13
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
nick1816
In the given figure AB is the diameter of the circle, whose center is O. Point C lies inside the circle such that ∠ACB=120 degrees. Also, OD is perpendicular to BC and length of OD is 1.5 cm. Find the length of AC?

A. \(\frac{3\sqrt{3}}{2}\)
B. 3
C. \(2\sqrt{3}\)
D. \(3\sqrt{3}\)
E. 6
Show more


Extend BC to meet the circle at E, and join AE.
\(\angle BEA\) is 90 as it is an angle on the diameter AB.
Therefore, AE||OD, as angle AEB and ODB are 90, and AE is double of OD, since BOD and ABE are similar triangles in the ratio 1:2=BO:BA.

Take triangle ACE.
Angle AEB= angle AEC = 90, as it is opposite the diameter AB.
Angle AEC=180-120=60.

Triangle AEC thus is 30-60-90 triangle.
Now AE opposite 60 degree angle is 3, so hypotenuse \(AC=\frac{2*3}{\sqrt{3}}=2\sqrt{3}\), as the sides are in ratio 1:sqrt3:2

C
Attachments

Untitled (5).png
Untitled (5).png [ 6.54 KiB | Viewed 3976 times ]

User avatar
hellothere88
User avatar
Joined: 18 Dec 2017
Last visit: 25 Jun 2022
Posts: 158
Own Kudos:
22
Given Kudos: 13
Posts: 158
Kudos: 22
In the given figure AB is the diameter of the circle, whose center is 27 Nov 2021, 03:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
nick1816
In the given figure AB is the diameter of the circle, whose center is O. Point C lies inside the circle such that ∠ACB=120 degrees. Also, OD is perpendicular to BC and length of OD is 1.5 cm. Find the length of AC?

A. \(\frac{3\sqrt{3}}{2}\)
B. 3
C. \(2\sqrt{3}\)
D. \(3\sqrt{3}\)
E. 6


Extend BC to meet the circle at E, and join AE.
Now AE||OD and double of OD, since BOD and ABE are similar triangles in the ratio 1:2=BO:BA.

Take triangle ACE.
Angle AEB= angle AEC = 90, as it is opposite the diameter AB.
Angle AEC=180-120=60.

Triangle AEC thus is 30-60-90 triangle.
Now AE opposite 60 degree angle is 3, so hypotenuse \(AC=\frac{2*3}{\sqrt{3}}=2\sqrt{3}\), as the sides are in ratio 1:sqrt3:2

C
Show more

how can it be AE||OD?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,237
Own Kudos:
1,158
Posts: 39,237
Kudos: 1,158
In the given figure AB is the diameter of the circle, whose center is 08 Aug 2025, 03:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113495 posts