Last visit was: 14 Jul 2024, 09:19 It is currently 14 Jul 2024, 09:19
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# The figure shows the intersection of a Square ABCD and a Circle. What

SORT BY:
Tags:
Show Tags
Hide Tags
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1895
Own Kudos [?]: 5778 [16]
Given Kudos: 238
WE:General Management (Education)
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1895
Own Kudos [?]: 5778 [12]
Given Kudos: 238
WE:General Management (Education)
Manager
Joined: 02 Sep 2019
Posts: 174
Own Kudos [?]: 259 [5]
Given Kudos: 28
Location: India
Schools: ISB'22
General Discussion
Intern
Joined: 11 Dec 2018
Posts: 12
Own Kudos [?]: 14 [0]
Given Kudos: 6
Location: United States (NC)
Schools: Harvard '23
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]

I'm assuming in the given diagram the diameter passes through the intersection of the diagonals:

a= side of the square
d=diameter of the circle
Requirement is to find 4a ?
= 4(d-x)

1) x=1
for x=1 perimeters =4(d-1)
multiple answers as d changes hence insufficient.

2) This basically gives product information. In a square diagonal are perpendicular. Not sufficient.
Current Student
Joined: 13 Apr 2019
Posts: 236
Own Kudos [?]: 65 [0]
Given Kudos: 309
Location: India
GMAT 1: 710 Q49 V36
GPA: 3.85
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
Here lets start by considering radius of circle as r. Let O be the center of circle and let M be the midpoint of side BC where Perpendicular from O meets BC.
By applying right angle property
(OB)^2 = (BM)^2 + (OM)^2
r^2 = (BM)^2 + (r-x)^2
on solving, we get (BM)^2 = x(2r-x)

since from 1 we know the value of x, we get value of (BM)^2 as 2r-1

so we cannot find the perimeter of square just from 1

(2) since its told that abcd is a square, we can already infer what is given in 2

Taking both 1 and 2, still we donot have enough information to find the value of r so answer is E
Intern
Joined: 15 Apr 2017
Posts: 35
Own Kudos [?]: 22 [0]
Given Kudos: 30
GMAT 1: 630 Q49 V27
GMAT 2: 710 Q50 V37
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
Ans: A
(1): from the mid point of the circle O draw radius to point B and C .Since the triangle OBC is an isosceles triangle with angle BOC = 90 degree. We can say sin 45 = OB/OX.
Now we can find radius and hence the perimeter.
(2). This is a redundant info . Its given that the figure is square which implies that diagonals will intersect at 90 degree.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 7963
Own Kudos [?]: 4214 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
#1
X=1 ;
insufficient as we dont know the center of circle also X=1 is the highest point of circle from square
#2
AC and BD are perpendicular to each other
the lines will intersect at center at 90* , but center of circle is not clear ; insufficient
from 1 &2
we can determine the sides of the digonals using 45:45:90 ; but will have unknow value of distance from center to circle side X=1
radius ; a+1 ; side of square ; 2a and perimeter ; 8a ; but value of a is not know
insufficient
IMO E

The figure shows the intersection of a Square ABCD and a Circle. What is the Perimeter of the Square ABCD?
1) X = 1
2) AC and BD are perpendicular to each other
Current Student
Joined: 06 Feb 2016
Status:On the journey of achieving
Affiliations: Senior Manager, CA by profession, CFA(USA) Level 2
Posts: 250
Own Kudos [?]: 170 [0]
Given Kudos: 148
Location: India
Concentration: Finance, Finance
GMAT 1: 560 Q44 V23
GMAT 2: 530 Q39 V24
GMAT 3: 580 Q46 V24 (Online)
GMAT 4: 640 Q50 V26
GPA: 3.82
WE:Other (Commercial Banking)
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
Let us look at each statements one by one

1) X = 1
This statement does not provides us any information which will provide us the dimensions of the square, we cannot arrive at any side dimension length of the square hence statement 1 alone is not sufficient

2) AC and BD are perpendicular to each other

This statement does not provides us any information which will provide us the dimensions of the square, hence statement 1 alone is not sufficient

Even when we combine information in both the statements together, it won't give us any information about square dimensions or of the circle, hence both statements together are also not sufficient.
Answer is Option E, even both the statements together are also not sufficient.
Director
Joined: 22 Feb 2018
Posts: 784
Own Kudos [?]: 1059 [0]
Given Kudos: 135
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
The figure shows the intersection of a Square ABCD and a Circle. What is the Perimeter of the Square ABCD?

Tricky one for me, still i'll try.

1) X = 1,
Insufficient as we can't find the radius of the circle, which can give us diameter of the circle, which in turn could help to find side or diagonal of square.

2) AC and BD are perpendicular to each other
It implies that diagonals pass through the center of the circle. But still we can't find the radius/diameter of the circle/diagonal of the square/side of square. Hence insufficient.

1) + 2)
Square is inscribed from the circle as AC and BD are perpendicular to each other. Still can not find the side of square. Hence insufficient.

Imo. E
Current Student
Joined: 18 Feb 2019
Posts: 34
Own Kudos [?]: 34 [0]
Given Kudos: 205
Location: India
GMAT 1: 660 Q47 V34
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]

EXPLANATION:

Please refer to the attached figure:
We have assumed a radius is drawn from B and C, meeting at the point which is coolinear to the point x distance is separated from the square. Hence, if the total distance is R, the point till the square edge (where x distance is separated from the circle), is r - x.

We can see, perimeter is:
r + k + 2l + r + k + 2l.

Also, we know, $$l = \sqrt{r^2 - (r-1)^2 }$$
Hence, L equals, $$\sqrt{2r - 1 }$$

Hence, solving the equation, we get perimeter as function of R as:
$$4r - 2 + 4\sqrt{2r-1}$$

Since the value of R can vary, the perimeter can vary and have more than one answer.
Attachments

File comment: Diagram

IMG_20191208_184450__01.jpg [ 1.58 MiB | Viewed 5569 times ]

Manager
Joined: 09 Dec 2019
Posts: 123
Own Kudos [?]: 173 [0]
Given Kudos: 5
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
For every square and circle which exist as shown in the figure, distance x will be unique and no two combination of square and circle can have same value of x.

(1) For x=1, we have a unique figure and thus the perimeter of the square can be determined.
Therefore, statement 1 is sufficient.

(2) AC and BD are perpendicular to each other
ABCD is a square AC and BD are always perpendicular to each other.
Not sufficient.

Intern
Joined: 22 May 2019
Posts: 5
Own Kudos [?]: 8 [0]
Given Kudos: 23
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
jhavyom can you explain how R+Y =2a in your explanation
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1895
Own Kudos [?]: 5778 [0]
Given Kudos: 238
WE:General Management (Education)
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
As per the jhyavyom solution, Side of the square is taken as 2a
Hence R+2a = side of the square = 2a

I hope it is clear, feel free to tag me in case of any doubt.

Happy Learning

saiprasanna wrote:
jhavyom can you explain how R+Y =2a in your explanation
Manager
Joined: 28 Jan 2017
Posts: 56
Own Kudos [?]: 48 [0]
Given Kudos: 217
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
Please expand on: R + y = 2a

How can that be true if R^2 = a^2 + y^2?

gmatbusters jhavyom
Intern
Joined: 13 Feb 2020
Posts: 2
Own Kudos [?]: 4 [0]
Given Kudos: 6
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
GMATBusters
sorry for this but couldnt understand how E lie on the diameter of the circle
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1895
Own Kudos [?]: 5778 [0]
Given Kudos: 238
WE:General Management (Education)
The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
By symmetry, it lies on diameter. It can be proved but better to use the principle of symmetry in GMAT.
Also, since the dimensioning line has 2 arrows, it means the max distance between the circle and circle, which is when E lies on diameter (otherwise the exact point on circle must have been specified).

sudhirgmat1 wrote:
GMATBusters
sorry for this but couldnt understand how E lie on the diameter of the circle
Joined: 19 Sep 2018
Posts: 90
Own Kudos [?]: 66 [0]
Given Kudos: 945
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
Hi GMATBusters,

I had a doubt regarding the symmetry used here. We need to assume that the figure drawn is symmetrical?
Because based on that assumption, we get that EC and EB are S/2 and E lies on the diameter of the circle. I didn't make the assumption and ended up choosing E.
In what situations do we need to assume that the figure given is symmetrical?

Thanks and Regards,
Udit
Non-Human User
Joined: 09 Sep 2013
Posts: 33966
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: The figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
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 figure shows the intersection of a Square ABCD and a Circle. What [#permalink]
Moderator:
Math Expert
94342 posts