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In the figure, AB and CD are the diameters of the circle. Wh
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02 Oct 2018, 11:18
02 Oct 2018, 11:18
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93% (01:05) correct
6% (00:48) wrong based on 33 sessions
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#GREpracticequestin n the figure, AB and CD are the diameters of the circle.jpg [ 36.55 KiB | Viewed 5137 times ]
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°
Re: In the figure, AB and CD are the diameters of the circle. Wh
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04 Oct 2018, 09:33
04 Oct 2018, 09:33
2
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
<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
Attachments
circlex.jpg [ 25.67 KiB | Viewed 6466 times ]
Re: In the figure, AB and CD are the diameters of the circle. Wh
[#permalink]
04 Oct 2018, 11:48
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
