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.
In the figure above, the triangle ABC is inscribed in the circle; the
[#permalink]
27 Sep 2023, 03:07
27 Sep 2023, 03:07
Expert Reply
00:00
Question Stats:
38% (01:31) correct
61% (01:36) wrong based on 21 sessions
Hide Show timer Statistics
Attachment:
GRe Circumference of the circle.jpg [ 9.96 KiB | Viewed 2297 times ]
In the figure above, the triangle ABC is inscribed in the circle; the ratio of the sides BC, AC, and AB is 3 : 4 : 5 and the perimeter of the triangle is 48.
Quantity A |
Quantity B |
Circumference of the circle |
\(20 \pi\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: In the figure above, the triangle ABC is inscribed in the circle; the
[#permalink]
27 Sep 2023, 06:50
27 Sep 2023, 06:50
I keep getting 20pi. What am I doing wrong?
Re: In the figure above, the triangle ABC is inscribed in the circle; the
[#permalink]
27 Sep 2023, 09:08
27 Sep 2023, 09:08
1
Expert Reply
Let the length of the sides BC, AC and AB, respectively be 3x, 4x and 5x, where x is a constant of proportionality.
We see that: (5x)^2 = (3x^2) + (4x)^2 => Triangle ABC is right-angled at C.
=> AB is the diameter of the circle (since the diameter subtends 90° at the circumference)
Sum of the three sides of the triangle = 3x + 4x + 5x = 12x.
Since the perimeter of the triangle is 48, we have 12x = 48 = > x = 4 = > Diameter of the circle = AB = 5x = 20
= > Radius of the circle 20 /2 = 10
=> Circumference of the circle \(= 2.7 \pi \times 10 = 20 \pi\)
We see that: (5x)^2 = (3x^2) + (4x)^2 => Triangle ABC is right-angled at C.
=> AB is the diameter of the circle (since the diameter subtends 90° at the circumference)
Sum of the three sides of the triangle = 3x + 4x + 5x = 12x.
Since the perimeter of the triangle is 48, we have 12x = 48 = > x = 4 = > Diameter of the circle = AB = 5x = 20
= > Radius of the circle 20 /2 = 10
=> Circumference of the circle \(= 2.7 \pi \times 10 = 20 \pi\)
