Last visit was: 25 Apr 2026, 01:06 It is currently 25 Apr 2026, 01:06
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
705-805 (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,114
 [12]
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,822
Kudos: 811,114
 [12]
What is the area of the triangle PQR in the circle shown above? 05 Sep 2018, 23:40
1
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

55% (02:35) correct 45% (02:23) wrong based on 149 sessions

History

Date
Time
Result
Not Attempted Yet

What is the area of the triangle PQR in the circle shown above?


(1) ac = 100

(2) \(bc = 5\sqrt{100}\)

Show Spoiler
Attachment:
image010.jpg
image010.jpg [ 4.79 KiB | Viewed 3917 times ]
ShowHide Answer
Official Answer
C
User avatar
ravikumarmishra
User avatar
Joined: 10 Aug 2009
Last visit: 11 Apr 2019
Posts: 51
Own Kudos:
18
 [1]
Given Kudos: 89
Products:
My Reviews
GMAT 1: 640 Q48 V31
Posts: 51
Kudos: 18
 [1]
What is the area of the triangle PQR in the circle shown above? 06 Sep 2018, 00:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
using both equations you can cancel out c and get the ratio of a AND b. so we cannot find exact values of a, b and c, hence insufficient. it should be E.


Sent from my iPhone using GMAT Club Forum
avatar
bbegumbayar
avatar
Joined: 10 Aug 2018
Last visit: 12 Dec 2019
Posts: 1
Given Kudos: 9
Posts: 1
Kudos: 0
What is the area of the triangle PQR in the circle shown above? 06 Sep 2018, 02:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is the point btw P and R the origin of the circle? Can we know it without explanation?

If it is the origin, we also know that a.c=b^2
User avatar
PKN
User avatar
Joined: 01 Oct 2017
Last visit: 11 Oct 2025
Posts: 809
Own Kudos:
1,637
 [3]
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 809
Kudos: 1,637
 [3]
What is the area of the triangle PQR in the circle shown above? 07 Sep 2018, 02:46
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
bbegumbayar
Is the point btw P and R the origin of the circle? Can we know it without explanation?

If it is the origin, we also know that a.c=b^2
Show more

Property of right angled triangle:-
If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
Hence, \(b^2=a*c\)------(a)

The point between P and R is not the center of the circle.

Question stem:- Area of triangle PQR?
Or, \(\frac{1}{2} (a+c)*b=?\)
For this, we must know the unique values of a,b, and c.

St1:- ac = 100
Or, \(b^2=ac=100\)
Or, b=10
But notice that a and c have more than one value, such as (a=25,c=4), (a=50, c=2)
So, the value of area is not unique.
Insufficient.

st2:- \(bc=5\sqrt{100}=50\)
Value of 'a' is unknown.
Insufficient.

Combined, b=10, ac=100,and bc=50
So, we have c=5, a=20.
Hence, area can be determined.
Sufficient.

Ans. (C)
User avatar
swim2109
User avatar
Joined: 09 Oct 2017
Last visit: 04 Apr 2024
Posts: 239
Own Kudos:
127
Given Kudos: 64
Location: Pakistan
Concentration: Finance, Strategy
Schools: Columbia CBS '24 (S) Fuqua '24 (WL) Marshall '24 (D) Sloan '24 (WA) Tepper '24 (WL) McCombs '24 Johnson '24 (A) Wharton '25
GMAT 1: 640 Q48 V31
GRE 1: Q169 V160
GPA: 2.83
Products:
My Reviews
Schools: Columbia CBS '24 (S) Fuqua '24 (WL) Marshall '24 (D) Sloan '24 (WA) Tepper '24 (WL) McCombs '24 Johnson '24 (A) Wharton '25
GMAT 1: 640 Q48 V31
GRE 1: Q169 V160
Posts: 239
Kudos: 127
What is the area of the triangle PQR in the circle shown above? 21 Sep 2021, 09:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel can you put the official answer explanation.
avatar
ZodiacZ
avatar
Joined: 28 Aug 2019
Last visit: 18 Sep 2022
Posts: 1
Given Kudos: 74
Posts: 1
Kudos: 0
What is the area of the triangle PQR in the circle shown above? 15 Oct 2021, 08:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
It is nowhere given that 'a+c' is the diameter of the circle. Hence the answer should be E.
User avatar
swim2109
User avatar
Joined: 09 Oct 2017
Last visit: 04 Apr 2024
Posts: 239
Own Kudos:
127
Given Kudos: 64
Location: Pakistan
Concentration: Finance, Strategy
Schools: Columbia CBS '24 (S) Fuqua '24 (WL) Marshall '24 (D) Sloan '24 (WA) Tepper '24 (WL) McCombs '24 Johnson '24 (A) Wharton '25
GMAT 1: 640 Q48 V31
GRE 1: Q169 V160
GPA: 2.83
Products:
My Reviews
Schools: Columbia CBS '24 (S) Fuqua '24 (WL) Marshall '24 (D) Sloan '24 (WA) Tepper '24 (WL) McCombs '24 Johnson '24 (A) Wharton '25
GMAT 1: 640 Q48 V31
GRE 1: Q169 V160
Posts: 239
Kudos: 127
What is the area of the triangle PQR in the circle shown above? 15 Oct 2021, 23:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PKN
bbegumbayar
Is the point btw P and R the origin of the circle? Can we know it without explanation?

If it is the origin, we also know that a.c=b^2

Property of right angled triangle:-
If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
Hence, \(b^2=a*c\)------(a)

The point between P and R is not the center of the circle.

Question stem:- Area of triangle PQR?
Or, \(\frac{1}{2} (a+c)*b=?\)
For this, we must know the unique values of a,b, and c.

St1:- ac = 100
Or, \(b^2=ac=100\)
Or, b=10
But notice that a and c have more than one value, such as (a=25,c=4), (a=50, c=2)
So, the value of area is not unique.
Insufficient.

st2:- \(bc=5\sqrt{100}=50\)
Value of 'a' is unknown.
Insufficient.

Combined, b=10, ac=100,and bc=50
So, we have c=5, a=20.
Hence, area can be determined.
Sufficient.

Ans. (C)
Show more


How is b^2=ac? Bunuel please put up the official answer of this
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,978
Own Kudos:
1,117
Posts: 38,978
Kudos: 1,117
What is the area of the triangle PQR in the circle shown above? 26 Jun 2023, 10:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109822 posts
kingbucky
498 posts
Gmat860sanskar
212 posts