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# In the circle above with center O, x =

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In the circle above with center O, x = [#permalink]

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16 Nov 2017, 00:53
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Question Stats:

97% (00:15) correct 3% (00:00) wrong based on 35 sessions

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In the circle above with center O, x =

(A) 60
(B) 50
(C) 45
(D) 30
(E) 20

[Reveal] Spoiler:
Attachment:

2017-11-16_1237_002.png [ 8 KiB | Viewed 453 times ]
[Reveal] Spoiler: OA

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In the circle above with center O, x = [#permalink]

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16 Nov 2017, 01:29
It should be 60, as the radius are equal so other angle is also x and when all three angles are equal then it's equilateral.
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Re: In the circle above with center O, x = [#permalink]

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16 Nov 2017, 03:18
Option A ...becoz all three angles would be equal
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Re: In the circle above with center O, x = [#permalink]

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16 Nov 2017, 08:32

Let the other 2 end points of the triangle be A and B. because the angles at both A and O are equal, the corresponding sides OA and AB are equal. Already OA = OB since both of them are the radius of the circle. Hence OAB is an equilateral triangle and thus all angles are equal and = 60 degree.

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In the circle above with center O, x = [#permalink]

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16 Nov 2017, 10:34
Bunuel wrote:

In the circle above with center O, x =

(A) 60
(B) 50
(C) 45
(D) 30
(E) 20

[Reveal] Spoiler:
Attachment:
2017-11-16_1237_002.png

Two sides of the triangle are radii, hence of equal length.

The $$x$$ close to the edge of the circle is opposite from a radius. The unmarked angle is also opposite from a radius. Angles opposite equal sides are equal. So all three angles = x

3x = 180
x = 60

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Re: In the circle above with center O, x = [#permalink]

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16 Nov 2017, 11:41
so its a equilateral triangle

60
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Re: In the circle above with center O, x = [#permalink]

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17 Nov 2017, 13:36
Bunuel wrote:

In the circle above with center O, x =

(A) 60
(B) 50
(C) 45
(D) 30
(E) 20

[Reveal] Spoiler:
Attachment:
2017-11-16_1237_002.png

We see that two sides of the triangle are radii, and since one of the corresponding angles is x, the other must also be x, and thus all three angles are x, and so we have three 60-degree angles.

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Re: In the circle above with center O, x =   [#permalink] 17 Nov 2017, 13:36
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