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

 It is currently 20 Jan 2019, 05:25

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

# If ∠ D C B is a right angle, then A C =

Author Message
TAGS:

### Hide Tags

Manager
Joined: 01 May 2016
Posts: 82
Location: United States
GPA: 3.8
If ∠ D C B is a right angle, then A C =  [#permalink]

### Show Tags

11 Feb 2018, 20:16
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:22) correct 34% (02:30) wrong based on 53 sessions

### HideShow timer Statistics

Attachment:

1.png [ 6.1 KiB | Viewed 509 times ]

If ∠ D C B is a right angle, then A C =

a 7

b 3+3√3

c 8

d 4+3√2

e 3+4√2

_________________

TD

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
If ∠ D C B is a right angle, then A C =  [#permalink]

### Show Tags

11 Feb 2018, 20:50
1
Attachment:

1.png [ 7.85 KiB | Viewed 488 times ]

In Triangle DCB(right-angled triangle), $$DB^2 = (4\sqrt{2})^2 + (4\sqrt{2})^2 = 64$$ -> DB = $$\sqrt{64} = 8$$

Triangles DXA and AXB are similar(SAS), therefore DX = XB = 4

In Triangle DXA, Side $$AX = \sqrt{5^2 - 4^2} = \sqrt{25 - 16} = \sqrt{9} = 3$$
In Triangle DXC, Side $$XC = \sqrt{(4\sqrt2)^2 - 4^2} = \sqrt{16} = 4$$

Therefore, $$AC = AX + XC = 3+4$$ = 7(Option A)

_________________

You've got what it takes, but it will take everything you've got

Manager
Joined: 15 Feb 2018
Posts: 195
Re: If ∠ D C B is a right angle, then A C =  [#permalink]

### Show Tags

20 Dec 2018, 13:52
All this the same as pushpitkc, therefore DX = XB = 4

Recognise triangle DXA as a 3, 4, 5 right angle triangle. Therefore AX=3
Recognise triangle DXC as a 45, 45, 90 right angle triangle (angle C has been bisected, X is 90º, so part of D is also 45º). Again, this is a triangle to recognise. Hypotenuse is 4√2, so legs are 4.

4+3=7

These two, plus the 30-60-90 right angle triangle ones that very much should be memorised
Re: If ∠ D C B is a right angle, then A C = &nbs [#permalink] 20 Dec 2018, 13:52
Display posts from previous: Sort by