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# In the figure attached, point O is the center of the circle

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In the figure attached, point O is the center of the circle [#permalink]  16 Jan 2011, 16:56
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66% (03:31) correct 33% (01:33) wrong based on 1 sessions
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
[Reveal] Spoiler: OA

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Advanced Triangles.png [ 36.77 KiB | Viewed 4282 times ]

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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  16 Jan 2011, 19:07
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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

It goes like this -

In triangle OAB , Angle O + Angle A + Angle B = 180 -------1
OA = OB (Radius) => Angle A = Angle B

In triangle ACB, Angle C = Angle O + Angle OAC (Sum of interior opposite angles)
=> Angle ACB = 2x;
Also, AC = AB => Angle ACB = Angle ABC = 2x each

Thus Angle A = Angle B = 2x each.

So, substituting in 1

5x = 180 => x = 36 deg.

This will help.
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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  17 Jan 2011, 19:38
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Amazing question...kinda a very good revision of my triagnometry
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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  18 Jan 2011, 20:51
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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 [ 9.23 KiB | Viewed 4163 times ]

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
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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  19 Jan 2011, 22:38
Cool, but i think its an ez 600 question. isnt it?
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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  19 Jan 2011, 23:57
in your original diagram OA and OB don't appear to be radii - the end points are off the circle... without getting them to be equal I dont think you can answer this question
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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  20 Jan 2011, 00:03
I agree. i assumed that A and B are on the circle.
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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  10 Mar 2011, 14:03
angle oac=x
angle acb=2x=angle b=2x=a (as oa and ob are radii)
so in triangle oab x+2x+3x=180
x=36
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Re: Quant Rev #161 Advanced Triangles Problem [#permalink]  11 Mar 2011, 01:14
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

The figure attached is ambiguous. A needs to be shown on the circle, or at least it should be mentioned that A is also a point on the circle. If A is any point inside the circle, you cant solve this question from given information.
Re: Quant Rev #161 Advanced Triangles Problem   [#permalink] 11 Mar 2011, 01:14
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