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03 Apr 2020, 04:27
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
71% (02:08) correct
29%
(02:04)
wrong
based on 69
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ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then what is the value of ∠BCD (in degrees) ?
A. 75
B. 90
C. 105
D. 120
E. 150
Are You Up For the Challenge: 700 Level Questions
A. 75
B. 90
C. 105
D. 120
E. 150
Are You Up For the Challenge: 700 Level Questions
03 Apr 2020, 16:53
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∠CAD = 1/2 (∠COD)
{The angle subtended by an arc of a circle at its center is twice of the angle it subtends anywhere on the circle's circumference.}
∠CAD = 60
Hence ∠BAD = 60+30=90
∠BAD + ∠BCD = 180
{the sum of a pair of opposite angles of a cyclic quadrilateral is 180}
∠BCD = 180-90 = 90
{The angle subtended by an arc of a circle at its center is twice of the angle it subtends anywhere on the circle's circumference.}
∠CAD = 60
Hence ∠BAD = 60+30=90
∠BAD + ∠BCD = 180
{the sum of a pair of opposite angles of a cyclic quadrilateral is 180}
∠BCD = 180-90 = 90
Bunuel
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03 Apr 2020, 18:57
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OD = OC (Radius of circle)
So, angle (ODC) = angle (OCD) = 30 deg
Angle (DOA) = 60 degrees
Angle (BAC) = 30 degrees (Given)
OA = OD (radius of circle)
Angle (ODA) = angle (OAD) = 60 deg
Sum of Opposite angles in a cyclic quad are 180 deg
Angle (BAD) + angle (BCD) = 180
So, angle (BCD) = 90 deg
correct answer is B
So, angle (ODC) = angle (OCD) = 30 deg
Angle (DOA) = 60 degrees
Angle (BAC) = 30 degrees (Given)
OA = OD (radius of circle)
Angle (ODA) = angle (OAD) = 60 deg
Sum of Opposite angles in a cyclic quad are 180 deg
Angle (BAD) + angle (BCD) = 180
So, angle (BCD) = 90 deg
correct answer is B
