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Question

ABCD is a cyclic quadrilateral PQ is a tangent at B . If DBQ =  65 , then BCD is  

 

 



Your Answer
A

35°

Your Answer
B

85° 

Correct Answer
C

115° 

Your Answer
D

90°


Solution

The correct option is C

115° 


Join OB and OD 

We know that OB is perpendicular to PQ

OBD = OBQ - DBQ

OBD = 90 – 65

OBD =  25

OB = OD (radius)

OBD = ODB =  25

In ODB

OBD + ODB + BOD =  180

25 + 25 + BOD =  180

BOD =  130

BAD = 12 BOD

(Angle subtended by a chord on the center is double the angle subtended on the circle)

BAD = 12 ( 130)

BAD =  65

ABCD is a cyclic quadrilateral

BCD + BAD =  180

BCD + 65 =  180

BCD =  115

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