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Updated on: 24 Feb 2018, 00:34
Originally posted by AccipiterQ on 21 Oct 2013, 08:36.
Last edited by Bunuel on 24 Feb 2018, 00:34, edited 2 times in total.
Last edited by Bunuel on 24 Feb 2018, 00:34, edited 2 times in total.
Edited the question.
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Rectangle ABCD is inscribed in circle P. What is the area of circle P?
(1) The area of rectangle ABCD is 100.
(2) Rectangle ABCD is a square.
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AccipiterQ
21 Oct 2013, 08:42
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AccipiterQ
Rectangle ABCD is inscribed in circle P. What is the area of circle P?
(1) The area of rectangle ABCD is 100.
(2) Rectangle ABCD is a square.
(1) The area of rectangle ABCD is 100.
(2) Rectangle ABCD is a square.
1. area of rectangle ABCD is 100. If the rectangle is also a square, then you can solve. It doesn't say that though, so the rectangle could have a number of different side lengths. insufficient.
2. rectangle ABCD is a square. No values are given. Insufficient.
1&2 combined. the rectangle is also a square, meaning that all sides are length of 10. you can draw a line from a to c (which would be the cirlce's diameter), and form a right triangle, with two sides of 10, and AC (the hypothaneuse (sp??) being unknown).
10^2+10^2=X^2
200=X^2
X=\(\sqrt{200}\)
X=10*\(\sqrt{2}\)
so the diameter is 10*\(\sqrt{2}\)
since the radius is half the diamter you get 5*\(\sqrt{2}\)
area of a cirlce is pi*r^2, so pi*(5*\(\sqrt{2}\))^2
=pi*25*2
=50*pi
so 1&2 are sufficient.
21 Oct 2013, 09:14
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AccipiterQ
AccipiterQ
Rectangle ABCD is inscribed in circle P. What is the area of circle P?
(1) The area of rectangle ABCD is 100.
(2) Rectangle ABCD is a square.
1. area of rectangle ABCD is 100. If the rectangle is also a square, then you can solve. It doesn't say that though, so the rectangle could have a number of different side lengths. insufficient.
2. rectangle ABCD is a square. No values are given. Insufficient.
1&2 combined. the rectangle is also a square, meaning that all sides are length of 10. you can draw a line from a to c (which would be the cirlce's diameter), and form a right triangle, with two sides of 10, and AC (the hypothaneuse (sp??) being unknown).
10^2+10^2=X^2
200=X^2
X=\(\sqrt{200}\)
X=10*\(\sqrt{2}\)
so the diameter is 10*\(\sqrt{2}\)
since the radius is half the diamter you get 5*\(\sqrt{2}\)
area of a cirlce is pi*r^2, so pi*(5*\(\sqrt{2}\))^2
=pi*25*2
=50*pi
so 1&2 are sufficient.
When combined: the area of a square is (diagonal)^2/2, so we are given that (diagonal)^2/2=100 --> \(d=10\sqrt{2}\).
