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As shown in the figure, square ABCD is inscribed in a circle with
[#permalink]
30 Oct 2020, 09:24
30 Oct 2020, 09:24
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As shown in the figure, square ABCD is inscribed in a circle with circumference \(2π\sqrt{x}\) . What is the area of the shaded region in the diagram above?
(A) \(2x\)
(B) \(πx-2x\)
(C) \(πx-x\sqrt{2}\)
(D) \(\frac{3.507}{10.02}\)
(E) \(πx-x\sqrt{5}\)
Re: As shown in the figure, square ABCD is inscribed in a circle with
[#permalink]
30 Oct 2020, 09:29
30 Oct 2020, 09:29
Given: As shown in the figure, square ABCD is inscribed in a circle with circumference \(2π\sqrt{x}\) .
Asked: What is the area of the shaded region in the diagram above?
Radius of the circle = \(\sqrt{x}\)
Diagonal of square ABCD = \(2\sqrt{x}\)
Side of square ABCD = \(\sqrt{2x}\)
Area of square ABCD = 2x
IMO A
Asked: What is the area of the shaded region in the diagram above?
Radius of the circle = \(\sqrt{x}\)
Diagonal of square ABCD = \(2\sqrt{x}\)
Side of square ABCD = \(\sqrt{2x}\)
Area of square ABCD = 2x
IMO A
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Re: As shown in the figure, square ABCD is inscribed in a circle with
[#permalink]
30 Oct 2020, 20:56
30 Oct 2020, 20:56
Top Contributor
Kinshook wrote:
Given: As shown in the figure, square ABCD is inscribed in a circle with circumference \(2π\sqrt{x}\) .
Asked: What is the area of the shaded region in the diagram above?
Radius of the circle = \(\sqrt{x}\)
Diagonal of square ABCD = \(2\sqrt{x}\)
Side of square ABCD = \(\sqrt{2x}\)
Area of square ABCD = 2x
IMO A
Asked: What is the area of the shaded region in the diagram above?
Radius of the circle = \(\sqrt{x}\)
Diagonal of square ABCD = \(2\sqrt{x}\)
Side of square ABCD = \(\sqrt{2x}\)
Area of square ABCD = 2x
IMO A
Hi Kinshook. The question asks for the area of the shaded region.
Area of the shaded region = Area of the circle - Area of the square
Circumference = 2\(\pi\)r = 2\(\pi \sqrt{x}\)
r = \(\sqrt{x}\)
Area = \(\pi r^2 = \pi x\)
Diameter of the circle = diagonal of the square = 2\(\sqrt{x}\)
Diagonal of the square = \(\sqrt{2}\) * Side of the square
2\(\sqrt{x}\) = \(\sqrt{2}\) * Side of the square
Side = \(\sqrt{2x}\)
Area = 2x
Therefore the area of the shaded region = \(\pi x - 2x\)
Option B
Arun Kumar
