NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 18:35 It is currently 26 Apr 2024, 18:35
Decision Tracker
My Rewards
New posts
New comers' posts

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

If A and B are tangent to the circle with center O as shown in the fig

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619246 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
If A and B are tangent to the circle with center O as shown in the fig [#permalink] New post   14 Sep 2018, 01:54
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

44% (02:55) correct 56% (02:36) wrong based on 32 sessions
Hide Show timer Statistics

If A and B are tangent to the circle with center O as shown in the figure above, and AD has a length of 5 and AC has a length of 13, what is the radius of the circle?


A. 25/12

B. 65/12

C. \(\sqrt{34}\)

D. \(\sqrt{41}\)

E. \(\sqrt{50}\)


Show Spoiler
Attachment:
image036.jpg
image036.jpg [ 2.86 KiB | Viewed 2703 times ]
ShowHide Answer
Official Answer
B
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5962
Own Kudos [?]: 13391 [2]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If A and B are tangent to the circle with center O as shown in the fig [#permalink] New post   14 Sep 2018, 02:11
1
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:

If A and B are tangent to the circle with center O as shown in the figure above, and AD has a length of 5 and AC has a length of 13, what is the radius of the circle?


A. 25/12

B. 65/12

C. \(\sqrt{34}\)

D. \(\sqrt{41}\)

E. \(\sqrt{50}\)


Show Spoiler
Attachment:
The attachment image036.jpg is no longer available


Triangle ADC is a right angle triangle with AC = 13 and AD = 5 i.e. CD = 12

Triangles ACD and OAD are similar triangle as per the property derived in attachment
hence,
AD / CD = OA / AC
OA = Radius = (5/12)*13 = 65/12

Answer: option B
Attachments

File comment: www.GMATinsight.com
Geometry 7 Similar Triangle Latest.jpg
Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 2551 times ]

User avatar
B
hadimadi
Manager
Manager
Joined: 26 Oct 2021
Posts: 117
Own Kudos [?]: 27 [0]
Given Kudos: 95
Send PM
Re: If A and B are tangent to the circle with center O as shown in the fig [#permalink] New post   10 Feb 2022, 08:28
Hi,

definetly not easy, especially if one doesn't know about the alternate angle theorem. But applying the AAT, we can get the drawing below and the solution:
Attachments

IMG_20220210_162619.JPG
IMG_20220210_162619.JPG [ 3.58 MiB | Viewed 1873 times ]

avatar
B
abhi0888
Intern
Intern
Joined: 15 Feb 2022
Posts: 6
Own Kudos [?]: 1 [0]
Given Kudos: 206
Location: United States (TX)
Concentration: International Business, Technology
GMAT 1: 720 Q48 V40
GPA: 2.99
WE:Research (Manufacturing)
Send PM
If A and B are tangent to the circle with center O as shown in the fig [#permalink] New post   05 Apr 2022, 08:19
One more way of solving could be to compare the area of the AOC obtained as follows-

Area of AOC = AD*OC = AC*OA

Put AC = 13, AD = 5 and OC = (13^2 - OA^2)^1/2. upon solving you find OA = 65/12.

Posted from my mobile device
GMAT Club Bot
gmatclubot
If A and B are tangent to the circle with center O as shown in the fig [#permalink]
05 Apr 2022, 08:19
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions