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

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Math Expert
Joined: 02 Sep 2009
Posts: 44656
In the figure above, if RS is the diameter of the circle and ST = 2 [#permalink]

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23 Nov 2017, 23:22
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Question Stats:

86% (00:27) correct 14% (01:35) wrong based on 29 sessions

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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 [ 6.3 KiB | Viewed 632 times ]
[Reveal] Spoiler: OA

_________________
Intern
Joined: 24 Nov 2017
Posts: 3
In the figure above, if RS is the diameter of the circle and ST = 2 [#permalink]

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24 Nov 2017, 01:26
1
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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

Choice A
Intern
Joined: 16 Oct 2017
Posts: 30
Location: Ireland
Concentration: Healthcare, Finance
Re: In the figure above, if RS is the diameter of the circle and ST = 2 [#permalink]

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24 Nov 2017, 12:47
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Bunuel wrote:

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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