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Question

In the given diagram O is the center of the circle and CD is a tangent. CAB and ACD are supplementary to each other OAC = 30. Find the value of OCB:


A

30

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B

20

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C

60

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D

50

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Solution

The correct option is A

30



Since, OA = OC (Radii)

OAC = OCA = 30

Therefore
AOC = 180 - OAC - OCA
= 1803030 = 120

ABC = 12 AOC
[The angle at the centre is twice the angle at the circumference.]
= 12×120 = 60

CAB and ACD are supplementary AB is parallel to CD
ABC = BCD (Alternate interior angle)

BCD=60

From the figure,
ACB=ACO+OCB60°=30°+OCBOCB=60°30°=30°


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