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In the figure above, if RS is the diameter of the circle and ST = 2

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In the figure above, if RS is the diameter of the circle and ST = 2 [#permalink]

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In the figure above, if RS is the diameter of the circle and ST = 2, what is the area of the circle?

(A) 2π
(B) 2π√2
(C) 4π√2
(D) 8π
(E) 8π√2

[Reveal] Spoiler:
Attachment:
2017-11-23_2025_002.png
2017-11-23_2025_002.png [ 6.3 KiB | Viewed 632 times ]
[Reveal] Spoiler: OA

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In the figure above, if RS is the diameter of the circle and ST = 2 [#permalink]

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RST is a right isosceles triangle. Angles are 45, 45, and 90.

Sides opposite these angles are in the ratio 1 : 1 : √2.

ST is a side opposite one of the 45 degrees and measures 2 units.
Therefore, side RS opposite to 90 degrees will measure 2√2 units.

RS is the diameter of the circle = 2√2 units. So, radius of the circle is √2 units.
Area = π(√2)^2 = 2π

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Re: In the figure above, if RS is the diameter of the circle and ST = 2 [#permalink]

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New post 24 Nov 2017, 12:47
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Bunuel wrote:
Image
In the figure above, if RS is the diameter of the circle and ST = 2, what is the area of the circle?

(A) 2π
(B) 2π√2
(C) 4π√2
(D) 8π
(E) 8π√2

[Reveal] Spoiler:
Attachment:
2017-11-23_2025_002.png


\(RT = ST = 2\)
\(RS^2 = RT^2 + ST^2 = 4 + 4 = 8\)
\(RS = \sqrt{8}\)
\(\frac{RS}{2} = \frac{\sqrt{8}}{2} = r\)
\(\pi * r^2 = Area = \pi * \frac{8}{4} = 2\pi\)
Re: In the figure above, if RS is the diameter of the circle and ST = 2   [#permalink] 24 Nov 2017, 12:47
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In the figure above, if RS is the diameter of the circle and ST = 2

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