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

 It is currently 15 Oct 2019, 04:52

### 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

# The circle with center C shown above is tangent to both axes

Author Message
TAGS:

### Hide Tags

VP
Joined: 09 Mar 2016
Posts: 1230
The circle with center C shown above is tangent to both axes  [#permalink]

### Show Tags

02 Mar 2018, 11:18
Bunuel wrote:

The circle with center C shown above is tangent to both axes. If the distance from O to C is equal to k, what is the radius of the circle, in terms of k ?

(A) k
(B) $$\frac{k}{\sqrt{2}}$$
(C) $$\frac{k}{\sqrt{3}}$$
(D) $$\frac{k}{2}$$
(E) $$\frac{k}{3}$$

Look at the diagram below:
Attachment:
Circle2.png
Since OC=k, then $$r^2+r^2=k^2$$ --> $$r=\frac{k}{\sqrt{2}}$$.

Dear Bunuel, hello !

i know you are tired of my questions but i am sure you still can understand me

can you please explan why do you use this formula? $$r^2+r^2=k^2$$

from this post https://gmatclub.com/forum/math-coordin ... 87652.html

i know that the if the circle is centered at the origin (0, 0), then the equation simplifies to: $$x^2+y^2 = r^2$$ and in other cases

we use this formula In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that:

$$(x−a)^2+(y−b)^2=r$$
VP
Joined: 09 Mar 2016
Posts: 1230
Re: The circle with center C shown above is tangent to both axes  [#permalink]

### Show Tags

02 Mar 2018, 12:13
EMPOWERgmatRichC wrote:
Hi saiesta,

You have to combine 'like' terms before you take the square-root of both sides.

Here's a simple example that proves WHY:

$$\sqrt{4}$$ = 2

$$\sqrt{(2+2)}$$ does NOT = $$\sqrt{2}$$ + $$\sqrt{2}$$ though

$$\sqrt{2}$$ = about 1.4

2 does NOT equal 1.4 + 1.4

Knowing THAT, how would you write your equation now?

GMAT assassins aren't born, they're made,
Rich

Hello EMPOWERgmatRichC,

what do you mean by combining 'like' terms before you take the square-root of both sides dont understand ...
VP
Joined: 09 Mar 2016
Posts: 1230
The circle with center C shown above is tangent to both axes  [#permalink]

### Show Tags

03 Mar 2018, 13:28
Bunuel wrote:

The circle with center C shown above is tangent to both axes. If the distance from O to C is equal to k, what is the radius of the circle, in terms of k ?

(A) k
(B) $$\frac{k}{\sqrt{2}}$$
(C) $$\frac{k}{\sqrt{3}}$$
(D) $$\frac{k}{2}$$
(E) $$\frac{k}{3}$$

Look at the diagram below:
Attachment:
Circle2.png
Since OC=k, then $$r^2+r^2=k^2$$ --> $$r=\frac{k}{\sqrt{2}}$$.

Bunuel shouldnt we rationalise denominator $$r=\frac{k}{\sqrt{2}}$$.

for instance if we have $$\frac{\sqrt{6}}{\sqrt{2}}$$ = $$\frac{\sqrt{6}}{\sqrt{2}}$$ *$$\frac{\sqrt{2}}{\sqrt{2}}$$ = $$\frac{\sqrt{12}}{\sqrt{4}}$$
so we get $$\frac{\sqrt{12}}2$$

As you see in the denominator 2 is without radical sign, so why you didn't write it so ?

Another question sqrt of 2 is 1.4 you could write it so in the denominator too ? in which case you could write 1.4 ? can you please explain ? pleaseee:)
Non-Human User
Joined: 09 Sep 2013
Posts: 13157
Re: The circle with center C shown above is tangent to both axes  [#permalink]

### Show Tags

16 Mar 2019, 15:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The circle with center C shown above is tangent to both axes   [#permalink] 16 Mar 2019, 15:29

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by