Last visit was: 24 Nov 2024, 05:12 It is currently 24 Nov 2024, 05:12
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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
Your Progress

every week, we’ll send you an estimated GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

A circle with centre O and diameter PR is inscribed in quad

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

avatar
fdundo
Intern
Intern
Joined: 11 Jul 2019
Posts: 16
Own Kudos [?]: 117 [3]
Given Kudos: 0
Concentration: General Management, Social Entrepreneurship
GRE 1: Q162 V154
WE:Project Management (Internet and New Media)
Send PM
A circle with centre O and diameter PR is inscribed in quad [#permalink] New post   Updated on: 24 Sep 2019, 00:49
1
2
Bookmarks
00:00

Question Stats:

47% (02:08) correct 52% (02:25) wrong based on 19 sessions

Hide Show timer Statistics

Attachment:
geometry tough.jpeg
geometry tough.jpeg [ 12.75 KiB | Viewed 7008 times ]


A circle with center O and diameter PR is inscribed in quadrilateral ABCD. Find the value of x.

Show: :: OA
56°

Originally posted by fdundo on 23 Sep 2019, 22:02.
Last edited by Carcass on 24 Sep 2019, 00:49, edited 1 time in total.
Edited by Carcass
avatar
brkztrk
Intern
Intern
Joined: 12 Oct 2019
Posts: 11
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
Re: A circle with centre O and diameter PR is inscribed in quad [#permalink] New post   21 Oct 2019, 11:08
1
I am not sure about my approach but we know that if PR is diameter then PQR must be 90 degree so RPQ is 56. Since the RPQ and the x corresponds the same arc, they must be equal.
avatar
Aaka
Manager
Manager
Joined: 19 Jan 2020
Posts: 56
Own Kudos [?]: 67 [0]
Given Kudos: 0
Send PM
Re: A circle with centre O and diameter PR is inscribed in quad [#permalink] New post   30 Jul 2020, 06:13
Can someone please explain the solution to this problem?
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [2]
Given Kudos: 136
Send PM

Top Member of the Month
Re: A circle with centre O and diameter PR is inscribed in quad [#permalink] New post   30 Jul 2020, 07:09
2
fdundo wrote:
Attachment:
geometry tough.jpeg


A circle with center O and diameter PR is inscribed in quadrilateral ABCD. Find the value of x.

Show: :: OA
56°


This question tests a circle property known as the Tangent-Chord Theorem (aka the Alternate Segment Theorem)

Image

This property is NOT tested on the GRE, so this question is out of scope



.
avatar
S
void
Senior Manager
Senior Manager
Joined: 03 Dec 2020
Posts: 440
Own Kudos [?]: 61 [0]
Given Kudos: 68
Send PM
Re: A circle with centre O and diameter PR is inscribed in quad [#permalink] New post   09 Jan 2021, 11:40
its alternate angles....
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5043
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: A circle with centre O and diameter PR is inscribed in quad [#permalink] New post   06 Feb 2023, 05:08
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36370 [3]
Given Kudos: 25928
Send PM
A circle with centre O and diameter PR is inscribed in quadrilateral A [#permalink] New post   28 Jun 2023, 07:06
Expert Reply
3
Bookmarks
Attachment:
GRE A circle with centre O and diameter PR is inscribed in quadrilateral.jpg
GRE A circle with centre O and diameter PR is inscribed in quadrilateral.jpg [ 22.24 KiB | Viewed 1846 times ]


A circle with centre O and diameter PR is inscribed in quadrilateral ABCD. Find the value of x?

Show: ::
56



Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos

\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
avatar
Sakshil
Intern
Intern
Joined: 14 Jul 2023
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: A circle with centre O and diameter PR is inscribed in quadrilateral A [#permalink] New post   18 Jul 2023, 20:57
Can anyone explain this? I got angle p as 56 but how is it for x as well?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36370 [1]
Given Kudos: 25928
Send PM
A circle with centre O and diameter PR is inscribed in quadrilateral A [#permalink] New post   19 Jul 2023, 00:07
1
Expert Reply
In triangle OQR, OQ = OR. (Both OQ and OR are radii of given circle)
So, angle opposite to these two sides would also be equal.
So, we can say, in triangle OQR.
Angle OQR = Angle ORQ


Hence angle OQR = 34°
Now consider quadrilateral ABCD, Side AD of quadrilateral is tangent to the circle. We
know, the angle between the radius of a circle and tangent is 90°

So, we can say angle OQD = 90°
From the given figure, we can say angle OQD = angle OQR + angle RQD

Hence 90°= 𝑥° + 34°
Hence 𝑥°= 56°

Ans. (56)
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36370 [0]
Given Kudos: 25928
Send PM
A circle with centre O and diameter PR is inscribed i [#permalink] New post   14 Sep 2023, 02:00
Expert Reply
Image

A circle with centre O and diameter PR is inscribed in quadrilateral ABCD. Find the value of x?

Show: ::
56



Part of the project: The Butler-GRE Daily New Quant and Verbal Questions to Practice (2023) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Prep Club for GRE Bot
gmatclubot
A circle with centre O and diameter PR is inscribed i [#permalink]
14 Sep 2023, 02:00
Moderators:
adewale223
GRE Instructor
84 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1111 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact