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13 May 2021, 07:45
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Difficulty:
55%
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Question Stats:
50% (01:44) correct
50%
(01:46)
wrong
based on 36
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If E is a point on the circumference of the circle circumscribing square ABCD, as shown above, what is the value of x?
A. 45
B. 90
C. 120
D. 135
E. 270
Attachment:
1.png [ 7.47 KiB | Viewed 1626 times ]
13 May 2021, 08:02
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Join the two diagonals AC and BD and let they meet at center is O and which is also the center of circle since AC and BD will be the diameter if angle ABC is 90 degrees.therefore Angle ADB is 45 degrees.
Now, Angle AOB will be 90 degrees since diagonals of square are perpendicular to each other.
Now let chord AB make Angle ADB on the major segment which will be half of Angle AOB (property of circle).
Now since ADBE is a cyclic quadrilateral therefore sum of AngleAEB and Angle ADB I 180 degrees. Therefore, AEB = 135 degrees (180 - 45).
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Now, Angle AOB will be 90 degrees since diagonals of square are perpendicular to each other.
Now let chord AB make Angle ADB on the major segment which will be half of Angle AOB (property of circle).
Now since ADBE is a cyclic quadrilateral therefore sum of AngleAEB and Angle ADB I 180 degrees. Therefore, AEB = 135 degrees (180 - 45).
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13 May 2021, 08:09
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Since it is a square inscribed inside the circle, if we can join each edge of the square to form an octagon inscribed within the circle, then x is simply the interior angle of the octagon.
Therefore, each interior angle measures (n-2) * 180/n
i.e (8-2)*180/8 = 135 degrees
IMO D
Therefore, each interior angle measures (n-2) * 180/n
i.e (8-2)*180/8 = 135 degrees
IMO D
