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Question

In Fig. 10.16 OAB=30andOCB=57 Find BOCandAOC
426701_dab3133031ca4640b4c9114fba9b7f79.png

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Solution

OAB=30o and OCB=57o.
In AOB,
AO=OB [ Radius of a circle ]
OBA=BAO=30o [ Angles opposite to equal sides are equal ]
In AOB,
AOB+OBA+BAO=180o.
AOB+30o+30o=180o
AOB=180o30o30o
AOB=120o ----- ( 1 )
Now, in OCB,
OC=OB [ Radius of a circle ]
OBC=OCB=57o. [ Angles opposite to equal sides are equal ]
In OCB,
BOC+OCB+OBC=180o.
BOC+57o+57o=180o
BOC=180o114o
BOC=66o ------ ( 2 )
AOB=120o [ From ( 1 ) ]
AOC+COB=120o.
AOC+66o=120o
AOC=120o66o
AOC=54o


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