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25 Jul 2018, 02:44
Kudos
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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:
55%
(hard)
Question Stats:
64% (03:09) correct
36%
(02:28)
wrong
based on 70
sessions
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In the circle above, if OA and BC are parallel, and radius OA of the circle is 3, what is the length of minor arc AD?
A. \(\frac{3}{2}\pi\)
B. \(2\pi\)
C. \(\frac{5}{2}\pi\)
D. \(3\pi\)
E. \(6\pi\)
Attachment:
Untitled.png [ 13.32 KiB | Viewed 2881 times ]
25 Jul 2018, 03:08
Kudos
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Bunuel
Answer is C.
The angle subtended by ARC DC at point B is half of what it subtends at the centre ( given as 60 degrees). From this we can use the parallel lines to find the central angle who minor arc is asked.
Please see attached image for detailed explanation.
Regards,
Gladi
Attachments
IMG_20180725_153135.jpg [ 3.96 MiB | Viewed 2624 times ]
Bunuel
Given
(i) OA=OB=OC=OD=radius of circle=3 unit (It is infered that OBC is an isosceles triangle)
(ii)OA||BC
(iii) \(\angle{OCD}\)=60 degree
To find: Length of Minor arc AD ? (Minor arc=Arc AXD in figure) (Our aim is to determine \(\angle{AOD}\))
Refer to the enclosed figure, we have \(\angle{OBC}=30\) (As per given data(i))
We have \(\angle{AOB}=\angle{OBC}=30\) (As per given data (ii)) (OA||BC; so alternate angles are equal)
Also we have \(\angle{BOD}=180=\angle{AOB}+\angle{AOD}\) (supplementary angles; angles on a straight line(here diameter))
So, \(\angle{AOD}=180-30=150\)
Now, Arc AXD=\(2πr*\frac{150}{360}\)=\(2π*3*\frac{5}{12}\)=\(\frac{5}{2}\pi\)
Ans. (C)
Attachments
Arc.JPG [ 17.23 KiB | Viewed 2408 times ]
