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Question

In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent calculate the numerical value of x.


A

58

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B

98

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C

28

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D

50

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Solution

The correct option is A

58


In ΔOBC,OB=OC (radii of same circle)
OBC=OCB =2OBC
64=2OBC
OBC=642=32

Now in ΔABT,
BAT=90 (OAAT)
OBC or ABT=32
BAT+ABT+x=180
90+32+x=180
122+x=180
x=180122=58


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