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In the figure above, the triangle ABC is inscribed in the circle; the
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27 Sep 2023, 03:07
27 Sep 2023, 03:07
Expert Reply
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Question Stats:
36% (01:31) correct
63% (01:46) wrong based on 22 sessions
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GRe Circumference of the circle.jpg [ 9.96 KiB | Viewed 3203 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.
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
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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 \(= 2.7 \pi \times 10 = 20 \pi\)
