GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 04:56

### 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

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

# AB and CD are chords of the circle, and E and F are the midpoints of

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58428
AB and CD are chords of the circle, and E and F are the midpoints of  [#permalink]

### Show Tags

Updated on: 22 Jul 2019, 06:15
2
4
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:27) correct 44% (02:43) wrong based on 55 sessions

### HideShow timer Statistics

AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. If EF = 17, then what is radius of the circle?

(A) 10

(B) 12

(C) 13

(D) 15

(E) 25

Source: Nova GMAT
Difficulty Level: 700

Attachment:

#GREpracticequestion AB and CD are chords of the circle.jpg [ 17.99 KiB | Viewed 1147 times ]

_________________

Originally posted by Bunuel on 02 Apr 2019, 23:42.
Last edited by SajjadAhmad on 22 Jul 2019, 06:15, edited 1 time in total.
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: AB and CD are chords of the circle, and E and F are the midpoints of  [#permalink]

### Show Tags

03 Apr 2019, 11:46
1
From the figure
AE = BE = 5
CF = FD = 12
EF = 17
OE = x, Then OF = 17-x

OAE is a right angle triangle, Apply Pythagorean theorem,
OA = $$\sqrt{25+x^2}$$ = radius
Similarly, OCF is a right angle triangle, Apply Pythagorean theorem,
OC = $$\sqrt{(17-x)^2+144}$$ = radius

Equating both equations as both are the radii, we get
$$25+x^2 = 289+x^2-34x+144$$
34x = 408
x = 12 = OE, then OF = 5
OA = OC = $$\sqrt{25+144}$$ = 13

_________________
Press +1 Kudos If my post helps!
Intern
Joined: 18 Oct 2018
Posts: 16
Re: AB and CD are chords of the circle, and E and F are the midpoints of  [#permalink]

### Show Tags

Updated on: 11 Apr 2019, 12:39
2
Bunuel wrote:

AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. If EF = 17, then what is radius of the circle?

(A) 10

(B) 12

(C) 13

(D) 15

(E) 25

Attachment:
#GREpracticequestion AB and CD are chords of the circle.jpg

The hypotenuses of AEO and OCF must be the same (the radius) $$AO = OC$$. $$EF = 17$$; one can quickly see that $$OE=12$$ and $$OF = 5$$.
Pythagoras Theorem: $$25 + 144 = 169$$ --> Answer: C.
Realizing that $$AO = OC$$ and that the specific values for OE and OF can be determined quickly without any math saves a lot of time on this question.

Originally posted by Zoom96 on 07 Apr 2019, 15:28.
Last edited by Zoom96 on 11 Apr 2019, 12:39, edited 3 times in total.
Director
Joined: 27 May 2012
Posts: 903
Re: AB and CD are chords of the circle, and E and F are the midpoints of  [#permalink]

### Show Tags

11 Apr 2019, 05:58
Zoom96 wrote:
Bunuel wrote:

AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. If EF = 17, then what is radius of the circle?

(A) 10

(B) 12

(C) 13

(D) 15

(E) 25

Attachment:
#GREpracticequestion AB and CD are chords of the circle.jpg

The hypotenuses of AEO and OCF must be the same (the radius) $$AO = CD$$. $$EF = 17$$; one can quickly see that $$OE=12$$ and $$OF = 5$$.
Pythagoras Theorem: $$25 + 144 = 169$$ --> Answer: C.
Realizing that $$AO =CD$$ and that the specific values for OE and OF can be determined quickly without any math saves a lot of time on this question.

Hi Zoom96,
Can you please elaborate how AO=CD? Thank you.
_________________
- Stne
Intern
Joined: 18 Oct 2018
Posts: 16
Re: AB and CD are chords of the circle, and E and F are the midpoints of  [#permalink]

### Show Tags

11 Apr 2019, 12:41
stne wrote:
Zoom96 wrote:
Bunuel wrote:

AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. If EF = 17, then what is radius of the circle?

(A) 10

(B) 12

(C) 13

(D) 15

(E) 25

Attachment:
#GREpracticequestion AB and CD are chords of the circle.jpg

The hypotenuses of AEO and OCF must be the same (the radius) $$AO = CD$$. $$EF = 17$$; one can quickly see that $$OE=12$$ and $$OF = 5$$.
Pythagoras Theorem: $$25 + 144 = 169$$ --> Answer: C.
Realizing that $$AO =CD$$ and that the specific values for OE and OF can be determined quickly without any math saves a lot of time on this question.

Hi Zoom96,
Can you please elaborate how AO=CD? Thank you.

Oh yeah my bad, I of course meant $$AO = OC$$ (both are the radius). I just fixed it. Thanks.
Intern
Joined: 20 Jan 2019
Posts: 12
Re: AB and CD are chords of the circle, and E and F are the midpoints of  [#permalink]

### Show Tags

17 Apr 2019, 10:47
Can also be solved by estimating the value by range

The the vertical lines of 5 and 12 tell us that the radius is more than 12, but just slightly...
Manager
Joined: 10 Apr 2018
Posts: 245
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 680 Q48 V34
GPA: 3.3
AB and CD are chords of the circle, and E and F are the midpoints of  [#permalink]

### Show Tags

13 Oct 2019, 10:46
Bunuel wrote:

AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. If EF = 17, then what is radius of the circle?

(A) 10

(B) 12

(C) 13

(D) 15

(E) 25

Source: Nova GMAT
Difficulty Level: 700

Attachment:
#GREpracticequestion AB and CD are chords of the circle.jpg

Let OE = x, so OF = 17-x
As OAE is a right angle triangle, we get,
OA=$$(25+x^2)^{1/2}$$
Similarly, as OCF is a right angle triangle, we get,
OC = $$((17−x)^2+144)^{1/2}$$
$$(25+x^2)^{1/2}$$=$$((17−x)^2+144)^{1/2}$$
=> x=12=OE,
So, from triangle OAE, we get that, OA=13=Radius

Therefore, the answer is option C.
AB and CD are chords of the circle, and E and F are the midpoints of   [#permalink] 13 Oct 2019, 10:46
Display posts from previous: Sort by