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23 Apr 2011, 06:09
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
55% (01:36) correct
45%
(01:30)
wrong
based on 64
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If O is the centre of the circle and angle(AOC)=70. Find angle(ABC).
Q1.jpg [ 24.64 KiB | Viewed 31776 times ]
a) 110
b) 145
c) 40
d) 135
Attachment:
Q1.jpg [ 24.64 KiB | Viewed 31776 times ]
a) 110
b) 145
c) 40
d) 135
23 Apr 2011, 06:39
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maheshsrini
Given:
\(\angle{AOC_{(Arc \hspace{2} ABC)}}=70\)
"Angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle"
Central angle made by arc \(AC\), \(\angle{AOC_{(Arc \hspace{2} AC)}=360-\angle{AOC_{(Arc \hspace{2} ABC)}}=360-70=290\)
\(\angle{AOC_{(Arc \hspace{2} AC)}=2\angle{ABC}\)
\(\angle{ABC}=\frac{290}{2}=145^{\circ}\)
Ans: "B"
23 Apr 2011, 06:52
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I think we can use two triangles AOB and BOC
Let angle OAB be x and angle OCB be y. Angles opposite to radii will be equal.
angle OAB = angle OBA = x
angle OBC = angle OCB = y
We need the value of angle ABC = angle OBA + angle OBC = x + y
For the quadrilateral OABC sum of interior angle = 360
Hence x + x + y + y + 70 = 360
2x + 2y = 360 - 70
x + y = 145
Same answer as fluke!
Let angle OAB be x and angle OCB be y. Angles opposite to radii will be equal.
angle OAB = angle OBA = x
angle OBC = angle OCB = y
We need the value of angle ABC = angle OBA + angle OBC = x + y
For the quadrilateral OABC sum of interior angle = 360
Hence x + x + y + y + 70 = 360
2x + 2y = 360 - 70
x + y = 145
Same answer as fluke!
