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Question 20
In figure, OAB=30 and OCB=57. Find BOC and AOC.

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Solution

Given, OAB=30 and OCB=57
In ΔAOB,
AO = OB [both are the radius of the same circle]
OBA=BAO=30 [angles opposite to equal sides are equal]
AOB+OBA+BAO=180 [by angle sum property of a triangle]
AOB+30+30=180
AOB=1802(30)
AOB=18060=120...........(i)

Now, in ΔOCB,
OC = OB [both are the radius of a circle]
OBC=OCB=57 [angles opposite to equal sides are equal]
COB+OCB+CBO=180 [by angle sum property of triangle]
COB=180(OCB+OBC)
COB=180(57+57)
COB=180114=66

From Eq. (i) AOB=120
AOC+COB=120
AOC+66=120
AOC=12066=54

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