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23 Nov 2017, 23:22
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
82% (00:57) correct
18%
(02:43)
wrong
based on 45
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
Attachment:
2017-11-23_2025_002.png [ 6.3 KiB | Viewed 2581 times ]
24 Nov 2017, 01:26
Kudos
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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
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
24 Nov 2017, 12:47
Kudos
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Bunuel
\(RT = ST = 2\)
\(RS^2 = RT^2 + ST^2 = 4 + 4 = 8\)
\(RS = \sqrt{8}\)
\(\frac{RS}{2} = \frac{\sqrt{8}}{2} = r\)
\(\pi * r^2 = Area = \pi * \frac{8}{4} = 2\pi\)
