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In the figure, AB and CD are the diameters of the circle. Wh

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In the figure, AB and CD are the diameters of the circle. Wh [#permalink] New post   02 Oct 2018, 11:18
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In the figure, AB and CD are the diameters of the circle. What is the value of x ?

(A) 16°
(B) 18°
(C) 26°
(D) 32°
(E) 58°
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Re: In the figure, AB and CD are the diameters of the circle. Wh [#permalink] New post   04 Oct 2018, 09:33
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Notice that inscribed <CAB is \(1/2\) the central <COB. This is because both the angles are formed of the same arc.
<AOC is 116 degrees because angles in straight line add to 360 degrees.
<ODB is also x degrees because this is vertically opposite angle x.
At this point we have two triangles. AOC and DOB
These triangles are similar because both contains the two radius and one pair of angles between them is same.
From this x = 32 degrees
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Re: In the figure, AB and CD are the diameters of the circle. Wh [#permalink] New post   04 Oct 2018, 11:48
Carcass wrote:

In the figure, AB and CD are the diameters of the circle. What is the value of x ?

(A) 16°
(B) 18°
(C) 26°
(D) 32°
(E) 58°



AC and BD are the two chords of equal length (as they are formed by the two diameters)

We know the inscribed angle of two equal chords are equal,

so angle CAO = Angle ODB = x = 32 degree
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Re: In the figure, AB and CD are the diameters of the circle. Wh [#permalink] New post   13 Aug 2022, 02:21
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the figure, AB and CD are the diameters of the circle. Wh [#permalink]
13 Aug 2022, 02:21
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