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Question 9
Two chords AB and AC of a circle subtends angles equal to 90 and 150 respectively at the centre. Find BAC, if AB and AC lie on the opposite sides of the centre.


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Solution

In ΔBOA
OB = OA [both are the radius of circle]
OAB=OBA . . . . (i) [angles opposite to equal sides are equal]

In ΔOAB, OBA+OAB+AOB=180 [by angle sum property of a triangle]
OAB+OAB+90=180 [from Eq (i)]
2OAB=18090
2OAB=90
OAB=45

Now, in ΔAOC AO = OC [both are the radius of a circle]
OCA=OAC ............(ii) [angles opposite to equal sides are equal]
Also, AOC+OAC+OCA=180 [by angle sum property of a triangle]
150+2OAC=180 [from Eq. (ii)]
2OAC=180150
2OAC=30
OAC=15
BAC=OAB+OAC=45+15=60


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