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# In the figure above, point O is the center of the circle and

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8690
Location: Pune, India
Re: In the figure above, point O is the center of the circle and  [#permalink]

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06 May 2018, 07:53
1
dave13 wrote:
VeritasPrepKarishma wrote:
tonebeeze wrote:
In the figure attached, point O is the center of the circle and OC = AC = AB. What is the value of x (in degrees)?

a. 40
b. 36
c. 34
d. 32
e. 30

A small diagram helps:
Attachment:
Ques1.jpg

In the figure, you see (180 - 2x) + y = 180 (straight angle) so 2x = y

Also, the moment you see the circle and its two radii, mark them equal and the corresponding angles equal. (the red angle = blue angle)
x + 180 - 2y = y
5x = 180 (from above, y = 2x)
x = 36

VeritasPrepKarishma hello

cant understand the logic behind this (180 - 2x) + y = 180 (straight angle) so 2x = y

if you are deducting 2x from 180 then why are you adding y ? there are 2x and 2y right and how 2x = y

why triangle OAB an isosceles and not an equilateral

have a great wekkend

In triangle OAC, OC = AC
That is why angle COA = angle OAC = x
So angle OCA = 180 - x - x = 180 - 2x

Also AC = BC, so in triangle ACB,
angle ACB = angle CBA = y

Angles OCA and ACB form a straight angle so
180 - 2x + y = 180

In triangle OAB, OA = OB = radius of the circle. But these are not equal to AB (so not equilateral)
Note that AB is actually equal to OC (and AC). OC is less than the radius of the circle.
_________________

Karishma
Veritas Prep GMAT Instructor

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Joined: 14 Jul 2016
Posts: 8
Re: In the figure above, point O is the center of the circle and  [#permalink]

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07 Oct 2018, 10:25
From triangle OAC,
<AOC = <OAC = x degree. (since OC = AC)

And ext. <ACB = <AOC + <OAC = 2x degree.

Now from triangle ACB,

AC = AB , therefore <ABC = <ACB = 2x degree and <CAB = (180 - 4x) degree.

Now considering triangle OAB,
<BOA + <OAB + <ABO = 180
x + [x+180-4x] + 2x = 180

Where and why am I going wrong on this ?
Intern
Joined: 25 Mar 2018
Posts: 20
Location: India
Schools: ISB '20, NTU '20
GMAT 1: 720 Q47 V42
Re: In the figure above, point O is the center of the circle and  [#permalink]

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22 Oct 2018, 08:04
I think that you have not considered the fact that OC=OB since both are radii of the circle. That makes angle y= (180-4x)+x

==> 2x= (180-4x)+x = 180-3x

5x=180. So, x is 36.

In my opinion, the moment we get 180=180 kind of situation, we should think that y and x can be substituted not against each other but together to get a solution.
Re: In the figure above, point O is the center of the circle and &nbs [#permalink] 22 Oct 2018, 08:04

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