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

 It is currently 21 Apr 2019, 07:37

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

Points A and B are on a circle of radius 5 and AB = 6. Point C is the

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54376
Points A and B are on a circle of radius 5 and AB = 6. Point C is the  [#permalink]

Show Tags

27 Mar 2019, 21:07
00:00

Difficulty:

55% (hard)

Question Stats:

47% (01:58) correct 53% (02:34) wrong based on 17 sessions

HideShow timer Statistics

Points A and B are on a circle of radius 5 and AB = 6. Point C is the midpoint of the minor arc AB. What is the length of the line segment AC?

(A) $$\sqrt{10}$$

(B) 7/2

(C) $$\sqrt{14}$$

(D) $$\sqrt{15}$$

(E) 4

_________________
Intern
Joined: 27 Sep 2018
Posts: 37
Re: Points A and B are on a circle of radius 5 and AB = 6. Point C is the  [#permalink]

Show Tags

27 Mar 2019, 22:22
1
Let O be centre of the circle

As AB is the arc and it's midpoint is given as C. If we draw a perpendicular from to AB it will bisect the chord AB at D(assumed point) and meet C such that OC=5=OD+DC
NOW, TRIANGLE OAD is rt angled triangle
And we can find OD using Pythagoras OD=rt(5^2-3^2)=4

Similarly triangle ADC is also a rt angled triangle and we can find AC using Pythagoras, AC=rt(3^2+1^2)=rt10

Posted from my mobile device
Intern
Joined: 07 Oct 2018
Posts: 18
Re: Points A and B are on a circle of radius 5 and AB = 6. Point C is the  [#permalink]

Show Tags

28 Mar 2019, 03:29
chetan2u can you please explain this?
Math Expert
Joined: 02 Aug 2009
Posts: 7573
Points A and B are on a circle of radius 5 and AB = 6. Point C is the  [#permalink]

Show Tags

28 Mar 2019, 07:01
1
Shreshtha55 wrote:
chetan2u can you please explain this?

Let join AB, and CO. Now, CO will bisect AB in two halves of 6/2 or 3..
Now since C is in the middle, the other thing will be that the chord AB and radius OC will be perpendicular to each other.

So, take triangle ADO with hypotenuse as 5 and one side as 3, so sides are 3:4:5, so OD = 4.

Now let us take triangle ADC, again a right angled triangle. CD=5-4=1, and AD = 3, so AC = $$\sqrt{1^2+3^2}=\sqrt{10}$$.
Attachments

1111.png [ 55 KiB | Viewed 192 times ]

_________________
Director
Joined: 27 May 2012
Posts: 730
Re: Points A and B are on a circle of radius 5 and AB = 6. Point C is the  [#permalink]

Show Tags

28 Mar 2019, 12:17
chetan2u wrote:
Shreshtha55 wrote:
chetan2u can you please explain this?

Let join AB, and CO. Now, CO will bisect AB in two halves of 6/2 or 3..
Now since C is in the middle, the other thing will be that the chord AB and radius OC will be perpendicular to each other.

So, take triangle ADO with hypotenuse as 5 and one side as 3, so sides are 3:4:5, so OD = 4.

Now let us take triangle ADB, again a right angled triangle. BD=5-4=1, and AD = 3, so AC = $$\sqrt{1^2+3^2}=\sqrt{10}$$.

Hi chetan2u,
Thank you for your solution,but some portions are not clear, can you check , in the last line did you mean triangle ADC rather than ADB also did you mean CD rather than BD,

Thanks.
_________________
- Stne
Re: Points A and B are on a circle of radius 5 and AB = 6. Point C is the   [#permalink] 28 Mar 2019, 12:17
Display posts from previous: Sort by