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13 Oct 2022, 01:31
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
78% (01:21) correct
22%
(01:26)
wrong
based on 72
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of the circle with center C?
(1) Arc ADB has length 10π.
(2) The area of sector ACBE is twice the area of sector ACBD.
Attachment:
2022-09-26_17-15-47.png [ 7.58 KiB | Viewed 1916 times ]
13 Oct 2022, 01:52
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Bunuel
Solution:
Pre Analysis:
- We area asked the area of the circle
- There are two ways in which we can get the area
- Case 1: if we get the radius of the circle then we can apply the formula \(\pi r^2\) to get area
- Case 2: If we somehow get the angle x or 360 - x along with area of the sector or length of the arc
Attachment:
ircleds.png [ 6.75 KiB | Viewed 1566 times ]
Statement 1: Arc ADB has length 10π
- Accordign to this statement, \(\frac{x}{360} 2\pi r=10 \pi\) or \(r=\frac{5\times 360}{x}\)
- This will not give us the value of either r or x
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: The area of sector ACBE is twice the area of sector ACBD
- According to this statement, \(\frac{360-x}{360} \pi r^2=2\times \frac{x}{360} \pi r^2\)
\(⇒360-x=2x\)
\(⇒3x=360\)
\(⇒x=120\) - From this, we are getting the value of x. However, no information on the area of the sector or the length of the arc
- Thus, statement 2 alone is also not sufficient and we can eliminate option B
Combining:
- From statement 1, we get \(r=\frac{5\times 360}{x}\)
- From statement 2, we get \(x=120\) which we can plug and get the value or r and this our answer
Hence the right answer is Option C
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