NEW HERE? LEARN MORE
close
It is currently 21 Apr 2023, 01:52
Register
GMAT Club Tests
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

Circles

5 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
avatar
B
carpedeim
Intern
Intern
Joined: 20 May 2020
Posts: 2
Circles [#permalink] New post  21 May 2020, 01:35
1
Kudos
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

20% (00:06) correct 80% (01:04) wrong based on 5 sessions

Hide Show timer Statistics

Two tangents xy and xz are drawn from a point x to a circle with centre w. If the length of xz is 156 and the length yz is 120, what is the radius of the circle?

A) 65
B) 60
C) 70
D) 75

Posted from my mobile device
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
avatar
L
shameekv1989
Director
Director
Joined: 14 Dec 2019
Posts: 831
Location: Poland
Concentration: Entrepreneurship, Strategy
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 1: 640 Q49 V27
GMAT 2: 660 Q49 V31
GMAT 3: 720 Q50 V38
GPA: 4
WE:Engineering (Consumer Electronics)
GMAT ToolKit User Reviews Badge
Re: Circles [#permalink] New post  21 May 2020, 04:24
carpedeim wrote:
Two tangents xy and xz are drawn from a point x to a circle with centre w. If the length of xz is 156 and the length yz is 120, what is the radius of the circle?

A) 65
B) 60
C) 70
D) 75

Posted from my mobile device


Answer would be 65. It is based on 2 properties.

i) Tangents are perpendicular with the radius of the circle.
ii) 2 Tangents are equal in length originating from the same point outside the circle to that circle.

Using pythagorous theorem we can form separate equations to know the length of wx (center to outside point x). yz will be cut into half by this line wx.

Answer - A
_________________
"GIVE AND YOU SHALL RECEIVE"

Admitted/Waitlisted students are requested to give a brief of their profile over here :-
https://gmatclub.com/forum/profiles-of-admitted-applicants-2021-intake-340293.html
Signature Read More
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5000
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Reviews Badge
Circles [#permalink] New post  22 May 2020, 11:01
shameekv1989 wrote:
carpedeim wrote:
Two tangents xy and xz are drawn from a point x to a circle with centre w. If the length of xz is 156 and the length yz is 120, what is the radius of the circle?

A) 65
B) 60
C) 70
D) 75

Posted from my mobile device


Answer would be 65. It is based on 2 properties.

i) Tangents are perpendicular with the radius of the circle.
ii) 2 Tangents are equal in length originating from the same point outside the circle to that circle.

Using pythagorous theorem we can form separate equations to know the length of wx (center to outside point x). yz will be cut into half by this line wx.

Answer - A


Hi shameekv1989
Please explain your solution in detail for bold portion
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Signature Read More
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5000
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Reviews Badge
Re: Circles [#permalink] New post  22 May 2020, 11:22
carpedeim wrote:
Two tangents xy and xz are drawn from a point x to a circle with centre w. If the length of xz is 156 and the length yz is 120, what is the radius of the circle?

A) 65
B) 60
C) 70
D) 75

Posted from my mobile device


Given: Two tangents xy and xz are drawn from a point x to a circle with centre w.
Asked: If the length of xz is 156 and the length yz is 120, what is the radius of the circle?

Attachment:
Screenshot 2020-05-22 at 11.48.36 PM.png
Screenshot 2020-05-22 at 11.48.36 PM.png [ 37.57 KiB | Viewed 1119 times ]


Let radius be 65.

156^2 + 65^2 = 24336 + 4225 = 28561 = 169^2 = (104+65)^2

IMO A

I tried to solve this problem using quadratic equations, but could not solve it easily.
Putting values of radius and verifying solutions worked well.
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Signature Read More
avatar
B
talwarmeister
Intern
Intern
Joined: 30 May 2010
Posts: 17
Re: Circles [#permalink] New post  15 Jan 2023, 19:02
Here is a good solution for this https://gmatclub.com/forum/two-tangents ... 25192.html
GMAT Club Bot
gmatclubot
Re: Circles [#permalink]
15 Jan 2023, 19:02
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews

cron

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