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Re: Square ABCD is inscribed in circle O. What is the area of square regio
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21 Oct 2015, 22:28
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1. Area of circle = pi*r^2 = 64 pi => r= 8 Diameter = 2*8= 16 Diagonal of the square is equal to diameter of the circle. Now applying pythagorean theorem , Let s = side length (s)^2 + (s)^2 = (diagonal)^2 => 2 *(s)^2 = 256 =>(s)^2 =128
Sufficient.
2 . 2*pi*r= 16 * pi => r = 8 We can calculate the area as in 1 . Sufficient.
Answer D
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Re: Square ABCD is inscribed in circle O. What is the area of square regio
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22 Oct 2015, 03:16
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Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
Given: A square is inscribed in a circle. Therefore, the Diameter of circle = Diagonal of the square Area of \(square = \frac{diagonal^2}{2}\)
Hence, all we need to know is the diameter of the circle.
S1- Given the area of circle, We can obtain the radius and hence, the diameter. - Sufficient S2- Given the circumference, like S1 we can obtain diameter. - Sufficient
Re: Square ABCD is inscribed in circle O. What is the area of square regio
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22 Oct 2015, 06:20
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
Since, square ABCD is inscribed in the circle, the only way that is possible is when the diagonal of the square is equal to the diameter of the circle. AB\(\sqrt{2}\) = diameter of circle = 2r
1) Area of O is 64π, i.e. \(πr^2\) = 64π. From this we can find the radius of the circle, thus determine the diameter and thereby we can deduce the area of the square ABCD.
2) Circumference of O is 16π, i.e. 2πr = 16π. From this we deduce radius, r and finally the area of square ABCD.
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Re: Square ABCD is inscribed in circle O. What is the area of square regio
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23 Oct 2015, 00:25
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
Draw the circle and inscribe a square to see that: The radius of the circle is half of the square's diagonal and hence all you need to to know is the radius from the circle in order to calculate the area of the square.
Area of a square can be calculated as \(\frac{D^2}{2}\)
Statement 1: From this we can calculate the radius since r^2π=64π, therefore r = 8 Statement 2: From this we can too, calculate the radius 2rπ = 16π, therefore 2r=16, r = 8
From both statements we can calculate the diagonal = 16 (=2*r) and hence the area of the square.
Re: Square ABCD is inscribed in circle O. What is the area of square regio
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01 May 2016, 04:23
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
There is nothing to solve here. We know ABCD is inscribed so its vertices are on the circle and the diagonal is the diameter of the circle. Once we know the diameter of circle we can find the area = D1*D2/2. here diagonal 1=diagonal 2 because both are diameter of circle and diagonal of a square. 1. we can find the diameter from area. 2. we can find the diameter from circumference.
Re: Square ABCD is inscribed in circle O. What is the area of square regio
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31 Jul 2016, 22:58
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
The area of any square is also given by the formula \(\frac{diagonal^2}{2}\) In a square inscribed inside a circle the diagonal becomes equal to the diameter SO if we can figure out the radius we can double it to find the diameter and hence the diagonal of the square and finally the area
Option 1 ) gives us the area ; radius can be calculated easily ; SUFFICIENT Option 2) gives us the circumference ; again radius be calculated easily; SUFFICIENT
ANSWER IS D
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Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.
Re: Square ABCD is inscribed in circle O. What is the area of square regio
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31 Jul 2016, 23:00
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
The area of any square is also given by the formula \(\frac{(diagonal^2)}{2}\) In a square inscribed inside a circle, the diagonal of square is equal to the diameter of the circle SO if we can figure out the radius we can double it to find the diameter and using diameter we can figure the area of Square by using \(\frac{(diagonal^2)}{2}\)
Option 1 ) gives us the area ; radius can be calculated easily ; SUFFICIENT Option 2) gives us the circumference ; again radius be calculated easily; SUFFICIENT
ANSWER IS D
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.
Re: Square ABCD is inscribed in circle O. What is the area of square regio
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28 Apr 2018, 07:49
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
Bunuel, why should we assume the corners of the square touch the circle? It just says the square is inscribed, nothing about how the inscription is made. Maybe I'm just overthinking the wording, but it really bothers me it doesn't specifically say "Sqaure ABCD inscribed in circle O with corners of sqaure touching the outside of the circle.
Re: Square ABCD is inscribed in circle O. What is the area of square regio
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28 Apr 2018, 11:45
ahawkins wrote:
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?
(1) The area of circular region O is 64π. (2) The circumference of circle O is 16π.
Kudos for a correct solution.
Bunuel, why should we assume the corners of the square touch the circle? It just says the square is inscribed, nothing about how the inscription is made. Maybe I'm just overthinking the wording, but it really bothers me it doesn't specifically say "Sqaure ABCD inscribed in circle O with corners of sqaure touching the outside of the circle.
In geometry "inscribed" means drawing one shape inside another so that it just touches. It does not mean just inside.
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Re: Square ABCD is inscribed in circle O. What is the area of square regio
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11 Jun 2019, 01:53
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