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Question

In the given figure, ABCD is a rectangle, OB is the radius, PB is the tangent at point B and OBC=30. Then, the value of x is___.


Your Answer
A
90
Your Answer
B
30
Your Answer
C
110
Correct Answer
D
60

Solution

The correct option is D 60
Given: OBC  = 30 
Consider, ABC 
ABC  = OBC + OBA 
  ABC = 30 OBA      ---- (1)
ABCD is a rectangle
ABC  = 90
 9030 OBA       [from (1)]
  OBA = 9030
  OBA = 60

Now,
Consider OAB
OB = OA     [radius]
By Theorem - Angle opposite to equal sides of a triangle are equal.
  OAB =  OBA = 60        ----(2)
By Theorem- Sum of angles of a triangle = 180
  OAB +  OBA +  AOB =  180
2 OAB + x =  180     [from (2)]
2×60x =  180
 x180120
  x60

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