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AB is the chord of a circle with centreO...

AB is the chord of a circle with centreO. AB is produced to C, such that BC =OB, CO is joined and produced to meet the circle in D.
If `angle ACD=Y^@` and `angle AOD=x^@`, Prove that `x = 3y`.

Text Solution

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OB`=`BC`implies /_BOC = /_ BCO = y^(@)`.
Ext. `/_ OBA = /_ BOC + /_BCO = (2y^(@))`
`OA = OB implies /_ OAB = /_ OBA = (2y^(@))`
Ext. `/_ AOD = /_ OAC + /_ACO = /_ OAB + /_BCO = (3y^(@)) implies x= 3y`
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