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30 Jun 2021, 01:30
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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:
55%
(hard)
Question Stats:
67% (02:42) correct
33%
(02:55)
wrong
based on 51
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In the figure above O is the center of the circle and ∠A is a right angle. If AE=AB, and ∠EAB=90º, and BC=CD=DE, what is the value of x in the figure above?
A. 150
B. 152
C. 160
D. 164
E. 172
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1.png [ 11.44 KiB | Viewed 2513 times ]
30 Jun 2021, 09:54
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Angle COB = 60 degree
Angle OAB = Bisector of EAB = 45 degree
Angle AOB = 90 degree
x = 90 + 60 = 150 degree
A is the right answer IMO
Angle OAB = Bisector of EAB = 45 degree
Angle AOB = 90 degree
x = 90 + 60 = 150 degree
A is the right answer IMO
Bunuel
30 Jun 2021, 10:01
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Bunuel
IMO A, 2.30 min. Decent question.
Concepts used :
Angle made by diameter is 90'. And the converse is also true i,e. If a chord makes 90' angle then it must be diameter.
Follow the below-attached image for a better understanding.
As <BAE = 90', Hence BE must be diameter. So OB=OC=OD=OE=OA=r (radius)
If you closely observe the image, OED, ODC, OCB are concurrent triangles. (All sides are equal)
Similarly, OAE,OBA is concurrent.
Hence <COB=<DOC=<EOD=60', Stright line BE,
Similarly <EOA=<AOB=90'
x=<AOB+<COB=150'
Attachments
WhatsApp Image 2021-06-30 at 10.10.28 PM.jpeg [ 149.4 KiB | Viewed 2214 times ]
