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In the figure above, the triangle ABC is inscribed in the circle; the
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12 Sep 2023, 04:30
12 Sep 2023, 04:30
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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]
24 Sep 2023, 05:16
24 Sep 2023, 05:16
1
3k+5k+4k=48 then
k=4 and this is the maximum value 'k' can take so the triangle ABC stays inside of the circle(**).
also, AB can not be greater than the diameter of the circle (2*R), so:
5*k=<2*R
considering (**): 20=2*R
the Circumference is: 2*pi*radius, hence:
20*pi=2*R*pi
k=4 and this is the maximum value 'k' can take so the triangle ABC stays inside of the circle(**).
also, AB can not be greater than the diameter of the circle (2*R), so:
5*k=<2*R
considering (**): 20=2*R
the Circumference is: 2*pi*radius, hence:
20*pi=2*R*pi
Re: In the figure above, the triangle ABC is inscribed in the circle; the
[#permalink]
24 Sep 2023, 17:46
24 Sep 2023, 17:46
2
The ratio of the triangle is 3:4:5, and 48 is the perimeter, which means 5x + 3x + 4x = 48. 12x = 48, x = 4.
The 3:4:5 ratio means that the triangle is a right triangle. Because it's a right triangle, it's the largest triangle that can be inscribed in the circle and the hypotenuse is the diameter. Since x = 4, 5*4 = 20 and 20 is the diameter.
20/2 = 10 meaning 10 is the radius.
The circumference = 2 * pi * r
C = 2 * pi * 10 = 20 * pi
Answer choice C.
The 3:4:5 ratio means that the triangle is a right triangle. Because it's a right triangle, it's the largest triangle that can be inscribed in the circle and the hypotenuse is the diameter. Since x = 4, 5*4 = 20 and 20 is the diameter.
20/2 = 10 meaning 10 is the radius.
The circumference = 2 * pi * r
C = 2 * pi * 10 = 20 * pi
Answer choice C.
