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# In the figure above O is the center of the circle and ∠A is a right an

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
In the figure above O is the center of the circle and ∠A is a right an  [#permalink]

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08 Nov 2016, 00:06
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:39) correct 30% (02:37) wrong based on 82 sessions

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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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T6158.png [ 12.06 KiB | Viewed 1511 times ]

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In the figure above O is the center of the circle and ∠A is a right an  [#permalink]

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08 Nov 2016, 06:16
3
Since BAE = 90 degrees --> Line BOE = Diameter --> Angle BOE = 180

Refer to the below figure:
1. Triangles OAB and OAE are similar --> Angle BOE = 2y = 180 --> y = 90
2. Triangles OED, OCD and OCB are all similar --> Angle BOE = 3l = 180 --> l = 60

Angle x = l + y = 150

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In the figure above O is the center of the circle and ∠A is a right an  [#permalink]

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11 Mar 2018, 08:52
Attachment:

13.png [ 11.98 KiB | Viewed 555 times ]

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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TD

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: In the figure above O is the center of the circle and ∠A is a right an  [#permalink]

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11 Mar 2018, 09:15
Tridhipal wrote:
Attachment:
13.png

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

Join EB.. it will pass through centre of circle..
Now there two different chords..
1) EA=AB so they will subtend equal angle from centre =180/2=90
2) BC=CD=DE, do they will subtend equal angles = 180/3=60

X = 60+90=150

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: In the figure above O is the center of the circle and ∠A is a right an  [#permalink]

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11 Mar 2018, 10:09
Tridhipal wrote:
Attachment:
13.png

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

Merging topics. Please search before posting. Thank you.
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Re: In the figure above O is the center of the circle and ∠A is a right an   [#permalink] 11 Mar 2018, 10:09
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