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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 28Live Online Class with Top GRE Expert Mike Butville
08:00 PM EDT
-10:00 PM EDT
Top scores are possible when you enroll in a powerful GRE course, taught live online + 6 months access to TTP GRE OnDemand video courses included! Class starts Mon/Wed Sept. 28, 2026 - Dec. 9, 2026, 8:00pm-10:00pm EST
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Circle O has a diameter AB of length 10 cm. Two points P and Q lie on
[#permalink]
11 Mar 2022, 23:00
11 Mar 2022, 23:00
1
1
Bookmarks
00:00
Question Stats:
100% (02:21) correct
0% (00:00) wrong based on 5 sessions
Hide Show timer Statistics
Circle O has a diameter AB of length 10 cm. Two points P and Q lie on the circle such that the length of chord PB is 6 cm, and the length of chord AP is twice that of chord AQ. What is the length (in cm) of chord QB?
Show: ::
\(\sqrt{84}\) or \(9.16\)
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: Circle O has a diameter AB of length 10 cm. Two points P and Q lie on
[#permalink]
24 Mar 2022, 21:56
24 Mar 2022, 21:56
1
Bookmarks
KarunMendiratta wrote:
Circle O has a diameter AB of length 10 cm. Two points P and Q lie on the circle such that the length of chord PB is 6 cm, and the length of chord AP is twice that of chord AQ. What is the length (in cm) of chord QB?
Show: ::
\(\sqrt{84}\) or \(9.16\)
Refer to the figure below.
Use Thale's Theorem: if A, B, and P are distinct points on a circle where the line AB is a diameter, the angle APB is a right angle.
In △APB;
\(AB^2 = AP^2 + PB^2\)
\(10^2 = (2x)^2 + 6^2\)
\(2x = 8\)
\(x = 4\)
i.e. AQ = 4cm
Now, In △AQB;
\(AB^2 = AQ^2 + QB^2\)
\(10^2 = (x)^2 + QB^2\)
\(10^2 = 4^2 + QB^2\)
\(QB^2 = 84\)
\(QB = \sqrt{84}\)
Attachments
Circle O has a diameter AB of length 10 cm.png [ 5.54 KiB | Viewed 2855 times ]
gmatclubot
Re: Circle O has a diameter AB of length 10 cm. Two points P and Q lie on [#permalink]
24 Mar 2022, 21:56
Moderators:
